{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:GAGFGINQXVIVUNKRQSBV3PFRXS","short_pith_number":"pith:GAGFGINQ","canonical_record":{"source":{"id":"1504.05037","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-04-20T12:41:34Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"78063442dde24f5437a11d261969df6d2e4b55bfeec82fed3b0baa5477ee1903","abstract_canon_sha256":"c0a15e2ba3d419db44cd8ab8916c94b65d9250e0c1d2c7475aecd2bf77428842"},"schema_version":"1.0"},"canonical_sha256":"300c5321b0bd515a355184835dbcb1bcac6f4f72b54802abb22d0e77202597c3","source":{"kind":"arxiv","id":"1504.05037","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.05037","created_at":"2026-05-18T01:12:58Z"},{"alias_kind":"arxiv_version","alias_value":"1504.05037v3","created_at":"2026-05-18T01:12:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05037","created_at":"2026-05-18T01:12:58Z"},{"alias_kind":"pith_short_12","alias_value":"GAGFGINQXVIV","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GAGFGINQXVIVUNKR","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GAGFGINQ","created_at":"2026-05-18T12:29:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:GAGFGINQXVIVUNKRQSBV3PFRXS","target":"record","payload":{"canonical_record":{"source":{"id":"1504.05037","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-04-20T12:41:34Z","cross_cats_sorted":["math.CO"],"title_canon_sha256":"78063442dde24f5437a11d261969df6d2e4b55bfeec82fed3b0baa5477ee1903","abstract_canon_sha256":"c0a15e2ba3d419db44cd8ab8916c94b65d9250e0c1d2c7475aecd2bf77428842"},"schema_version":"1.0"},"canonical_sha256":"300c5321b0bd515a355184835dbcb1bcac6f4f72b54802abb22d0e77202597c3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:58.557010Z","signature_b64":"RyVec+2xJIzf2uuTXMaK7KcfOLfkCQbxPL36ZjNfcuGrQ5G8FEZu+577+iyG2oZNaSRJMHGiLlUn1XTZveg0AA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"300c5321b0bd515a355184835dbcb1bcac6f4f72b54802abb22d0e77202597c3","last_reissued_at":"2026-05-18T01:12:58.556651Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:58.556651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1504.05037","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:12:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Hru288dqnId1XRivEx6saIBviZ6r9DWvPDRhDT2g6b6TwtZJDrrLrd4IrTpVl/LrqASttXcmUhGKHDVKpRZ6Cg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T21:55:48.868662Z"},"content_sha256":"f9f34bdfde2f65545c0a2db2366677e4f0f422fe00bb3090e3446d241a478bbf","schema_version":"1.0","event_id":"sha256:f9f34bdfde2f65545c0a2db2366677e4f0f422fe00bb3090e3446d241a478bbf"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:GAGFGINQXVIVUNKRQSBV3PFRXS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Golod property for Stanley-Reisner rings in varying characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.AC","authors_text":"Lukas Katth\\\"an","submitted_at":"2015-04-20T12:41:34Z","abstract_excerpt":"We show that the Golod property of a Stanley-Reisner ring can depend on the characteristic of the base field. More precisely, for every finite set $T$ of prime numbers we construct simplicial complexes $\\Delta$ and $\\Gamma$, such that $\\mathbb{K}[\\Delta]$ is Golod exactly in the characteristics in $T$ and $\\mathbb{K}[\\Gamma]$ is Golod exactly in the characteristics not in $T$. Along the way, we show that a one-dimensional simplicial complex is Golod if and only if it is chordal."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05037","kind":"arxiv","version":3},"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":"2026-05-18T01:12:58Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UDTQjyhub/T6yMY5th/tpKI9BosVdAWn/YkVjJSQP+NEruCHMLMNa022RwD3bzKRQWB8Wza0S7h2dpJGHas2Dg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T21:55:48.869344Z"},"content_sha256":"25a43bb97bb71deb394b2d96a4592589040b2992a42d8ba44a2ffd497fadc494","schema_version":"1.0","event_id":"sha256:25a43bb97bb71deb394b2d96a4592589040b2992a42d8ba44a2ffd497fadc494"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GAGFGINQXVIVUNKRQSBV3PFRXS/bundle.json","state_url":"https://pith.science/pith/GAGFGINQXVIVUNKRQSBV3PFRXS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GAGFGINQXVIVUNKRQSBV3PFRXS/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":"2026-05-31T21:55:48Z","links":{"resolver":"https://pith.science/pith/GAGFGINQXVIVUNKRQSBV3PFRXS","bundle":"https://pith.science/pith/GAGFGINQXVIVUNKRQSBV3PFRXS/bundle.json","state":"https://pith.science/pith/GAGFGINQXVIVUNKRQSBV3PFRXS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GAGFGINQXVIVUNKRQSBV3PFRXS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:GAGFGINQXVIVUNKRQSBV3PFRXS","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":"c0a15e2ba3d419db44cd8ab8916c94b65d9250e0c1d2c7475aecd2bf77428842","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-04-20T12:41:34Z","title_canon_sha256":"78063442dde24f5437a11d261969df6d2e4b55bfeec82fed3b0baa5477ee1903"},"schema_version":"1.0","source":{"id":"1504.05037","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1504.05037","created_at":"2026-05-18T01:12:58Z"},{"alias_kind":"arxiv_version","alias_value":"1504.05037v3","created_at":"2026-05-18T01:12:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.05037","created_at":"2026-05-18T01:12:58Z"},{"alias_kind":"pith_short_12","alias_value":"GAGFGINQXVIV","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_16","alias_value":"GAGFGINQXVIVUNKR","created_at":"2026-05-18T12:29:22Z"},{"alias_kind":"pith_short_8","alias_value":"GAGFGINQ","created_at":"2026-05-18T12:29:22Z"}],"graph_snapshots":[{"event_id":"sha256:25a43bb97bb71deb394b2d96a4592589040b2992a42d8ba44a2ffd497fadc494","target":"graph","created_at":"2026-05-18T01:12:58Z","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":"We show that the Golod property of a Stanley-Reisner ring can depend on the characteristic of the base field. More precisely, for every finite set $T$ of prime numbers we construct simplicial complexes $\\Delta$ and $\\Gamma$, such that $\\mathbb{K}[\\Delta]$ is Golod exactly in the characteristics in $T$ and $\\mathbb{K}[\\Gamma]$ is Golod exactly in the characteristics not in $T$. Along the way, we show that a one-dimensional simplicial complex is Golod if and only if it is chordal.","authors_text":"Lukas Katth\\\"an","cross_cats":["math.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-04-20T12:41:34Z","title":"The Golod property for Stanley-Reisner rings in varying characteristic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.05037","kind":"arxiv","version":3},"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:f9f34bdfde2f65545c0a2db2366677e4f0f422fe00bb3090e3446d241a478bbf","target":"record","created_at":"2026-05-18T01:12:58Z","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":"c0a15e2ba3d419db44cd8ab8916c94b65d9250e0c1d2c7475aecd2bf77428842","cross_cats_sorted":["math.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-04-20T12:41:34Z","title_canon_sha256":"78063442dde24f5437a11d261969df6d2e4b55bfeec82fed3b0baa5477ee1903"},"schema_version":"1.0","source":{"id":"1504.05037","kind":"arxiv","version":3}},"canonical_sha256":"300c5321b0bd515a355184835dbcb1bcac6f4f72b54802abb22d0e77202597c3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"300c5321b0bd515a355184835dbcb1bcac6f4f72b54802abb22d0e77202597c3","first_computed_at":"2026-05-18T01:12:58.556651Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:58.556651Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"RyVec+2xJIzf2uuTXMaK7KcfOLfkCQbxPL36ZjNfcuGrQ5G8FEZu+577+iyG2oZNaSRJMHGiLlUn1XTZveg0AA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:58.557010Z","signed_message":"canonical_sha256_bytes"},"source_id":"1504.05037","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f9f34bdfde2f65545c0a2db2366677e4f0f422fe00bb3090e3446d241a478bbf","sha256:25a43bb97bb71deb394b2d96a4592589040b2992a42d8ba44a2ffd497fadc494"],"state_sha256":"bbbc66511df045c54ef4f6a91a43da9a9e51c2a9f87b197ad64e079d48936808"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"G3IMi0bw/9dHnL7OpNwD0XRuQU1HYPO8tfBLvbG6k/4JFYnEG5nVuKUwvjVwnOn+9fW69w+ABNj8VuKL8hfWCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T21:55:48.873120Z","bundle_sha256":"4cbf486cd6b20b367abb5a138e9f0ff7d26237520804616734fcc894b0b55e2f"}}