{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:7SFOP3UDFYWOLQMSO3TDFH5FQV","short_pith_number":"pith:7SFOP3UD","canonical_record":{"source":{"id":"1701.03180","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-01-11T22:26:59Z","cross_cats_sorted":[],"title_canon_sha256":"0554745b2929988fe1158e27aae0b14c5d33b20c28767b3877361ef35e8f3fe0","abstract_canon_sha256":"94ec21a8285e30d3bc2d37477308ffa30e1a354a52ad3bf8f2bb8174b785eb52"},"schema_version":"1.0"},"canonical_sha256":"fc8ae7ee832e2ce5c19276e6329fa5856fc4f0ef0f4387183d2e7bb3b1d14bb6","source":{"kind":"arxiv","id":"1701.03180","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.03180","created_at":"2026-05-18T00:52:58Z"},{"alias_kind":"arxiv_version","alias_value":"1701.03180v1","created_at":"2026-05-18T00:52:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.03180","created_at":"2026-05-18T00:52:58Z"},{"alias_kind":"pith_short_12","alias_value":"7SFOP3UDFYWO","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7SFOP3UDFYWOLQMS","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7SFOP3UD","created_at":"2026-05-18T12:31:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:7SFOP3UDFYWOLQMSO3TDFH5FQV","target":"record","payload":{"canonical_record":{"source":{"id":"1701.03180","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-01-11T22:26:59Z","cross_cats_sorted":[],"title_canon_sha256":"0554745b2929988fe1158e27aae0b14c5d33b20c28767b3877361ef35e8f3fe0","abstract_canon_sha256":"94ec21a8285e30d3bc2d37477308ffa30e1a354a52ad3bf8f2bb8174b785eb52"},"schema_version":"1.0"},"canonical_sha256":"fc8ae7ee832e2ce5c19276e6329fa5856fc4f0ef0f4387183d2e7bb3b1d14bb6","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:52:58.287433Z","signature_b64":"u4T4qdMAOPij6i+ZB5DFFjgfzfLhZw2OrQeKpYtr3RWaUVGVL8H1TUFfRqHLgnh91qOGaHEoZWH/uoyO5MisAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"fc8ae7ee832e2ce5c19276e6329fa5856fc4f0ef0f4387183d2e7bb3b1d14bb6","last_reissued_at":"2026-05-18T00:52:58.286957Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:52:58.286957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1701.03180","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":"2026-05-18T00:52:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"DZUsQIywNg7ZaJcrB2YV7yDdg6hcMq/wJE7ze5QbiTcFQgniakH+UF9a06pPX9MWug5WLsGZ6L1kTmybgpKhAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T10:29:36.192160Z"},"content_sha256":"c06608a0b7f9a6cd0127e1fd244d5dd697ec3da82a934276b9f504fecd112645","schema_version":"1.0","event_id":"sha256:c06608a0b7f9a6cd0127e1fd244d5dd697ec3da82a934276b9f504fecd112645"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:7SFOP3UDFYWOLQMSO3TDFH5FQV","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Artinian level algebras of socle degree 4","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Maria Evelina Rossi, Shreedevi K. Masuti","submitted_at":"2017-01-11T22:26:59Z","abstract_excerpt":"In this paper we study the O-sequences of the local (or graded) $K$-algebras of socle degree $4.$ More precisely, we prove that an O-sequence $h=(1, 3, h_2, h_3, h_4)$, where $h_4 \\geq 2,$ is the $h$-vector of a local level $K$-algebra if and only if $h_3\\leq 3 h_4.$ We also prove that $h=(1, 3, h_2, h_3, 1)$ is the $h$-vector of a local Gorenstein $K$-algebra if and only if $h_3 \\leq 3$ and $h_2 \\leq \\binom{h_3+1}{2}+(3-h_3).$ In each of these cases we give an effective method to construct a local level $K$-algebra with a given $h$-vector. Moreover we refine a result by Elias and Rossi by sho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.03180","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":"2026-05-18T00:52:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/KBG8mZoHXuwfdxuOreS5Vl6kIm5/3laMfNySsm6aXmavGWNX7Vu45dmVCgNZhQJ8cMaQInc2OfTCgPZOzqYDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T10:29:36.192526Z"},"content_sha256":"8cb5a64c90d32ee027772cee73e855b802decce47afa2a4ecabe53900619a510","schema_version":"1.0","event_id":"sha256:8cb5a64c90d32ee027772cee73e855b802decce47afa2a4ecabe53900619a510"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/7SFOP3UDFYWOLQMSO3TDFH5FQV/bundle.json","state_url":"https://pith.science/pith/7SFOP3UDFYWOLQMSO3TDFH5FQV/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/7SFOP3UDFYWOLQMSO3TDFH5FQV/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":"2026-06-11T10:29:36Z","links":{"resolver":"https://pith.science/pith/7SFOP3UDFYWOLQMSO3TDFH5FQV","bundle":"https://pith.science/pith/7SFOP3UDFYWOLQMSO3TDFH5FQV/bundle.json","state":"https://pith.science/pith/7SFOP3UDFYWOLQMSO3TDFH5FQV/state.json","well_known_bundle":"https://pith.science/.well-known/pith/7SFOP3UDFYWOLQMSO3TDFH5FQV/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:7SFOP3UDFYWOLQMSO3TDFH5FQV","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":"94ec21a8285e30d3bc2d37477308ffa30e1a354a52ad3bf8f2bb8174b785eb52","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-01-11T22:26:59Z","title_canon_sha256":"0554745b2929988fe1158e27aae0b14c5d33b20c28767b3877361ef35e8f3fe0"},"schema_version":"1.0","source":{"id":"1701.03180","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1701.03180","created_at":"2026-05-18T00:52:58Z"},{"alias_kind":"arxiv_version","alias_value":"1701.03180v1","created_at":"2026-05-18T00:52:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1701.03180","created_at":"2026-05-18T00:52:58Z"},{"alias_kind":"pith_short_12","alias_value":"7SFOP3UDFYWO","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_16","alias_value":"7SFOP3UDFYWOLQMS","created_at":"2026-05-18T12:31:05Z"},{"alias_kind":"pith_short_8","alias_value":"7SFOP3UD","created_at":"2026-05-18T12:31:05Z"}],"graph_snapshots":[{"event_id":"sha256:8cb5a64c90d32ee027772cee73e855b802decce47afa2a4ecabe53900619a510","target":"graph","created_at":"2026-05-18T00:52:58Z","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 the O-sequences of the local (or graded) $K$-algebras of socle degree $4.$ More precisely, we prove that an O-sequence $h=(1, 3, h_2, h_3, h_4)$, where $h_4 \\geq 2,$ is the $h$-vector of a local level $K$-algebra if and only if $h_3\\leq 3 h_4.$ We also prove that $h=(1, 3, h_2, h_3, 1)$ is the $h$-vector of a local Gorenstein $K$-algebra if and only if $h_3 \\leq 3$ and $h_2 \\leq \\binom{h_3+1}{2}+(3-h_3).$ In each of these cases we give an effective method to construct a local level $K$-algebra with a given $h$-vector. Moreover we refine a result by Elias and Rossi by sho","authors_text":"Maria Evelina Rossi, Shreedevi K. Masuti","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-01-11T22:26:59Z","title":"Artinian level algebras of socle degree 4"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1701.03180","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:c06608a0b7f9a6cd0127e1fd244d5dd697ec3da82a934276b9f504fecd112645","target":"record","created_at":"2026-05-18T00:52:58Z","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":"94ec21a8285e30d3bc2d37477308ffa30e1a354a52ad3bf8f2bb8174b785eb52","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2017-01-11T22:26:59Z","title_canon_sha256":"0554745b2929988fe1158e27aae0b14c5d33b20c28767b3877361ef35e8f3fe0"},"schema_version":"1.0","source":{"id":"1701.03180","kind":"arxiv","version":1}},"canonical_sha256":"fc8ae7ee832e2ce5c19276e6329fa5856fc4f0ef0f4387183d2e7bb3b1d14bb6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fc8ae7ee832e2ce5c19276e6329fa5856fc4f0ef0f4387183d2e7bb3b1d14bb6","first_computed_at":"2026-05-18T00:52:58.286957Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:52:58.286957Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"u4T4qdMAOPij6i+ZB5DFFjgfzfLhZw2OrQeKpYtr3RWaUVGVL8H1TUFfRqHLgnh91qOGaHEoZWH/uoyO5MisAg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:52:58.287433Z","signed_message":"canonical_sha256_bytes"},"source_id":"1701.03180","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c06608a0b7f9a6cd0127e1fd244d5dd697ec3da82a934276b9f504fecd112645","sha256:8cb5a64c90d32ee027772cee73e855b802decce47afa2a4ecabe53900619a510"],"state_sha256":"bd858ead587baaa6f61a7815015287dff0692090948017b4b6ba7d5c4971d939"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Fa6s1BMDUkx+6uDhHUVPFLCBkcGLd0Y4R4aDunpd0nCi3jwpVn6RHyxE1+gN1Hj9EWxkmK15AYsDODh2GVmlDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T10:29:36.194665Z","bundle_sha256":"b966737d4d9bc7c6adffc0b7d86bb310a23e3a135737a095e47b657a0082ac8e"}}