{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:JJ7RUOUCQ77XV2ELU2KUMSCAHP","short_pith_number":"pith:JJ7RUOUC","canonical_record":{"source":{"id":"1510.00676","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-10-02T18:31:44Z","cross_cats_sorted":[],"title_canon_sha256":"09d522d8da2fa5eed6d6ecbc098b98328180d657c01735349e39f41d6ab95c41","abstract_canon_sha256":"a6fe477292f5c8f35214ec682c1a3a4f28a027995f011bf32a652a3d07a7e744"},"schema_version":"1.0"},"canonical_sha256":"4a7f1a3a8287ff7ae88ba6954648403bd6614a9a23a3c1a08363acc01d461882","source":{"kind":"arxiv","id":"1510.00676","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.00676","created_at":"2026-05-18T01:31:12Z"},{"alias_kind":"arxiv_version","alias_value":"1510.00676v1","created_at":"2026-05-18T01:31:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.00676","created_at":"2026-05-18T01:31:12Z"},{"alias_kind":"pith_short_12","alias_value":"JJ7RUOUCQ77X","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JJ7RUOUCQ77XV2EL","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JJ7RUOUC","created_at":"2026-05-18T12:29:27Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:JJ7RUOUCQ77XV2ELU2KUMSCAHP","target":"record","payload":{"canonical_record":{"source":{"id":"1510.00676","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-10-02T18:31:44Z","cross_cats_sorted":[],"title_canon_sha256":"09d522d8da2fa5eed6d6ecbc098b98328180d657c01735349e39f41d6ab95c41","abstract_canon_sha256":"a6fe477292f5c8f35214ec682c1a3a4f28a027995f011bf32a652a3d07a7e744"},"schema_version":"1.0"},"canonical_sha256":"4a7f1a3a8287ff7ae88ba6954648403bd6614a9a23a3c1a08363acc01d461882","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:31:12.310656Z","signature_b64":"PTMUMBHMkTSoXCzdoM/gKWwwNOl/tmE5jk7VgpfWBESX9F7pfXONCC4YxQrC8ea1VmP/ZWAcEt9G7X4s/XecBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4a7f1a3a8287ff7ae88ba6954648403bd6614a9a23a3c1a08363acc01d461882","last_reissued_at":"2026-05-18T01:31:12.310013Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:31:12.310013Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.00676","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":"2026-05-18T01:31:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"f0zBlIqVfLL6yz+W1X+GB6ceNLB7D6QcsW5t+kwIwmzr2M/tfRK1S5rQiL2/7a9MIVvIUEkte5hn9KWtDsvaAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T19:30:00.662796Z"},"content_sha256":"376fde8126719cfab99c09823e0c26536a7429a0733d5bbbb4fbe7940c33d864","schema_version":"1.0","event_id":"sha256:376fde8126719cfab99c09823e0c26536a7429a0733d5bbbb4fbe7940c33d864"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:JJ7RUOUCQ77XV2ELU2KUMSCAHP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the degrees of relations on $x_1^{d_1}, \\ldots, x_n^{d_n}, (x_1+ \\ldots + x_n)^{d_{n+1}}$ in positive characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AC","authors_text":"Adela Vraciu","submitted_at":"2015-10-02T18:31:44Z","abstract_excerpt":"We give a formula for the smallest degree of a non-Koszul relation on $x_1^{d_1}, \\ldots, x_n^{d_n}, (x_1+\\ldots +x_n)^{d_{n+1}}\\in k[x_1, \\ldots, x_n]$ (under certain assumptions on $d_1, \\ldots, d_{n+1}$) where $k$ is a field of positive characteristic $p$. As an application of our result, we give a formula for the diagonal F-threshold of a diagonal hypersurface. Another application is a characterization, depending on the characteristic $p$ of $k$, of the values of $d_1, \\ldots, d_{n+1}$ (satisfying certain assumptions) such that the ring $k[x_1, \\ldots, x_{n+1}]/(x_1^{d_1}, \\ldots, x_{n+1}^"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00676","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":"2026-05-18T01:31:12Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yaVgA7mbOntYhrznkqdj7RJL5TgwaboAktKofvjejbKRmMFHT0+x+MKhQMyXgRiFIlv/+MyEWITFuuDkGIkDDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T19:30:00.663136Z"},"content_sha256":"4592431bde45ebda25193663ee2a954137d16036e6bdb2b9aea58d77c82a40a8","schema_version":"1.0","event_id":"sha256:4592431bde45ebda25193663ee2a954137d16036e6bdb2b9aea58d77c82a40a8"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JJ7RUOUCQ77XV2ELU2KUMSCAHP/bundle.json","state_url":"https://pith.science/pith/JJ7RUOUCQ77XV2ELU2KUMSCAHP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JJ7RUOUCQ77XV2ELU2KUMSCAHP/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":"2026-06-24T19:30:00Z","links":{"resolver":"https://pith.science/pith/JJ7RUOUCQ77XV2ELU2KUMSCAHP","bundle":"https://pith.science/pith/JJ7RUOUCQ77XV2ELU2KUMSCAHP/bundle.json","state":"https://pith.science/pith/JJ7RUOUCQ77XV2ELU2KUMSCAHP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JJ7RUOUCQ77XV2ELU2KUMSCAHP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:JJ7RUOUCQ77XV2ELU2KUMSCAHP","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":"a6fe477292f5c8f35214ec682c1a3a4f28a027995f011bf32a652a3d07a7e744","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-10-02T18:31:44Z","title_canon_sha256":"09d522d8da2fa5eed6d6ecbc098b98328180d657c01735349e39f41d6ab95c41"},"schema_version":"1.0","source":{"id":"1510.00676","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.00676","created_at":"2026-05-18T01:31:12Z"},{"alias_kind":"arxiv_version","alias_value":"1510.00676v1","created_at":"2026-05-18T01:31:12Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.00676","created_at":"2026-05-18T01:31:12Z"},{"alias_kind":"pith_short_12","alias_value":"JJ7RUOUCQ77X","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_16","alias_value":"JJ7RUOUCQ77XV2EL","created_at":"2026-05-18T12:29:27Z"},{"alias_kind":"pith_short_8","alias_value":"JJ7RUOUC","created_at":"2026-05-18T12:29:27Z"}],"graph_snapshots":[{"event_id":"sha256:4592431bde45ebda25193663ee2a954137d16036e6bdb2b9aea58d77c82a40a8","target":"graph","created_at":"2026-05-18T01:31:12Z","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 give a formula for the smallest degree of a non-Koszul relation on $x_1^{d_1}, \\ldots, x_n^{d_n}, (x_1+\\ldots +x_n)^{d_{n+1}}\\in k[x_1, \\ldots, x_n]$ (under certain assumptions on $d_1, \\ldots, d_{n+1}$) where $k$ is a field of positive characteristic $p$. As an application of our result, we give a formula for the diagonal F-threshold of a diagonal hypersurface. Another application is a characterization, depending on the characteristic $p$ of $k$, of the values of $d_1, \\ldots, d_{n+1}$ (satisfying certain assumptions) such that the ring $k[x_1, \\ldots, x_{n+1}]/(x_1^{d_1}, \\ldots, x_{n+1}^","authors_text":"Adela Vraciu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-10-02T18:31:44Z","title":"On the degrees of relations on $x_1^{d_1}, \\ldots, x_n^{d_n}, (x_1+ \\ldots + x_n)^{d_{n+1}}$ in positive characteristic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.00676","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":"sha256:376fde8126719cfab99c09823e0c26536a7429a0733d5bbbb4fbe7940c33d864","target":"record","created_at":"2026-05-18T01:31:12Z","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":"a6fe477292f5c8f35214ec682c1a3a4f28a027995f011bf32a652a3d07a7e744","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2015-10-02T18:31:44Z","title_canon_sha256":"09d522d8da2fa5eed6d6ecbc098b98328180d657c01735349e39f41d6ab95c41"},"schema_version":"1.0","source":{"id":"1510.00676","kind":"arxiv","version":1}},"canonical_sha256":"4a7f1a3a8287ff7ae88ba6954648403bd6614a9a23a3c1a08363acc01d461882","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4a7f1a3a8287ff7ae88ba6954648403bd6614a9a23a3c1a08363acc01d461882","first_computed_at":"2026-05-18T01:31:12.310013Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:31:12.310013Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"PTMUMBHMkTSoXCzdoM/gKWwwNOl/tmE5jk7VgpfWBESX9F7pfXONCC4YxQrC8ea1VmP/ZWAcEt9G7X4s/XecBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:31:12.310656Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.00676","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:376fde8126719cfab99c09823e0c26536a7429a0733d5bbbb4fbe7940c33d864","sha256:4592431bde45ebda25193663ee2a954137d16036e6bdb2b9aea58d77c82a40a8"],"state_sha256":"c31a6591b9099386ebee2cade966fec44a9cbacd66aac358957033b86b6cf0ce"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LH+IKgoPrulNUQfkYSZjJ9YzPbhPJBBVGkCNLKA+LW/tvgNW7KhIZqayXklOpJTkNLHvKDW46stelgfUJOhhDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T19:30:00.665077Z","bundle_sha256":"13d9507364c3547bf93d1724264fa8d0698b5aaf01d7f7ea17a8cba833f327cd"}}