{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:6JEB3G5BOCT4VKNVVCN3BLTEFX","short_pith_number":"pith:6JEB3G5B","canonical_record":{"source":{"id":"1412.7941","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-26T14:35:24Z","cross_cats_sorted":[],"title_canon_sha256":"dfcee9fcd1e2b6309d3fad1b75b3076c9d778bf168815c7c2580f99cc8beb755","abstract_canon_sha256":"7fe9dbd3c42d72a4fcc64127b27632d88ece29c26856c1efb26b4cd7c23b8520"},"schema_version":"1.0"},"canonical_sha256":"f2481d9ba170a7caa9b5a89bb0ae642dd29005608318c4e5e18b3859b4035b3f","source":{"kind":"arxiv","id":"1412.7941","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.7941","created_at":"2026-05-18T01:34:30Z"},{"alias_kind":"arxiv_version","alias_value":"1412.7941v3","created_at":"2026-05-18T01:34:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.7941","created_at":"2026-05-18T01:34:30Z"},{"alias_kind":"pith_short_12","alias_value":"6JEB3G5BOCT4","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6JEB3G5BOCT4VKNV","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6JEB3G5B","created_at":"2026-05-18T12:28:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:6JEB3G5BOCT4VKNVVCN3BLTEFX","target":"record","payload":{"canonical_record":{"source":{"id":"1412.7941","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-26T14:35:24Z","cross_cats_sorted":[],"title_canon_sha256":"dfcee9fcd1e2b6309d3fad1b75b3076c9d778bf168815c7c2580f99cc8beb755","abstract_canon_sha256":"7fe9dbd3c42d72a4fcc64127b27632d88ece29c26856c1efb26b4cd7c23b8520"},"schema_version":"1.0"},"canonical_sha256":"f2481d9ba170a7caa9b5a89bb0ae642dd29005608318c4e5e18b3859b4035b3f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:34:30.917190Z","signature_b64":"sea9mtziAJxDcPPugoD0V3dv6wMUwA7RTRWxiwpHcJdkpriCVkmMTwvcCbGYzWYXTiBAoWzkPWBmE29b2htNCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f2481d9ba170a7caa9b5a89bb0ae642dd29005608318c4e5e18b3859b4035b3f","last_reissued_at":"2026-05-18T01:34:30.916795Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:34:30.916795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1412.7941","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":"2026-05-18T01:34:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VkWjtMlFVB2/ahXfaZXRgTJzir4RpuB6NapJus+GwTqThq/3tLNr3qvCvZQZXstV4ceXw/BdhwopyNMvFYmEAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T20:57:46.709415Z"},"content_sha256":"e2250a222d2cf2605eca010a81c3999baddf610157d7ae66c0d2f332f3eb0f9a","schema_version":"1.0","event_id":"sha256:e2250a222d2cf2605eca010a81c3999baddf610157d7ae66c0d2f332f3eb0f9a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:6JEB3G5BOCT4VKNVVCN3BLTEFX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Quotients of schemes by $\\alpha_p$ or $\\mu_p$ actions in characteristic p>0","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Nikolaos Tziolas","submitted_at":"2014-12-26T14:35:24Z","abstract_excerpt":"This paper studies schemes X defined over a field of characteristic p>0 which admit a nontrivial $\\alpha_p$ or $\\mu_p$ action. In particular, the structure of the quotient map $X \\rightarrow Y$ is investigated. Information on local properties of the quotient Y, as singularities and local Picard groups, structure theorems for the quotient map and adjunction formulas for the quotient map are obtained."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7941","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":"2026-05-18T01:34:30Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FtKW4rthTPn6gTuTNuJ0ralVLSu5Yt1mjgi1Bi8vDHSCV5P1NQ5EedH0MrftNqLUqLtA25P3lVb3k53XIu4/CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T20:57:46.710136Z"},"content_sha256":"b07d20a8f3cb0d302aac8c2f38c89e953f6e39de879525cb7ae4241b9c54214a","schema_version":"1.0","event_id":"sha256:b07d20a8f3cb0d302aac8c2f38c89e953f6e39de879525cb7ae4241b9c54214a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6JEB3G5BOCT4VKNVVCN3BLTEFX/bundle.json","state_url":"https://pith.science/pith/6JEB3G5BOCT4VKNVVCN3BLTEFX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6JEB3G5BOCT4VKNVVCN3BLTEFX/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":"2026-06-08T20:57:46Z","links":{"resolver":"https://pith.science/pith/6JEB3G5BOCT4VKNVVCN3BLTEFX","bundle":"https://pith.science/pith/6JEB3G5BOCT4VKNVVCN3BLTEFX/bundle.json","state":"https://pith.science/pith/6JEB3G5BOCT4VKNVVCN3BLTEFX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6JEB3G5BOCT4VKNVVCN3BLTEFX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:6JEB3G5BOCT4VKNVVCN3BLTEFX","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":"7fe9dbd3c42d72a4fcc64127b27632d88ece29c26856c1efb26b4cd7c23b8520","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-26T14:35:24Z","title_canon_sha256":"dfcee9fcd1e2b6309d3fad1b75b3076c9d778bf168815c7c2580f99cc8beb755"},"schema_version":"1.0","source":{"id":"1412.7941","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1412.7941","created_at":"2026-05-18T01:34:30Z"},{"alias_kind":"arxiv_version","alias_value":"1412.7941v3","created_at":"2026-05-18T01:34:30Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.7941","created_at":"2026-05-18T01:34:30Z"},{"alias_kind":"pith_short_12","alias_value":"6JEB3G5BOCT4","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_16","alias_value":"6JEB3G5BOCT4VKNV","created_at":"2026-05-18T12:28:16Z"},{"alias_kind":"pith_short_8","alias_value":"6JEB3G5B","created_at":"2026-05-18T12:28:16Z"}],"graph_snapshots":[{"event_id":"sha256:b07d20a8f3cb0d302aac8c2f38c89e953f6e39de879525cb7ae4241b9c54214a","target":"graph","created_at":"2026-05-18T01:34:30Z","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":"This paper studies schemes X defined over a field of characteristic p>0 which admit a nontrivial $\\alpha_p$ or $\\mu_p$ action. In particular, the structure of the quotient map $X \\rightarrow Y$ is investigated. Information on local properties of the quotient Y, as singularities and local Picard groups, structure theorems for the quotient map and adjunction formulas for the quotient map are obtained.","authors_text":"Nikolaos Tziolas","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-26T14:35:24Z","title":"Quotients of schemes by $\\alpha_p$ or $\\mu_p$ actions in characteristic p>0"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.7941","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:e2250a222d2cf2605eca010a81c3999baddf610157d7ae66c0d2f332f3eb0f9a","target":"record","created_at":"2026-05-18T01:34:30Z","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":"7fe9dbd3c42d72a4fcc64127b27632d88ece29c26856c1efb26b4cd7c23b8520","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-12-26T14:35:24Z","title_canon_sha256":"dfcee9fcd1e2b6309d3fad1b75b3076c9d778bf168815c7c2580f99cc8beb755"},"schema_version":"1.0","source":{"id":"1412.7941","kind":"arxiv","version":3}},"canonical_sha256":"f2481d9ba170a7caa9b5a89bb0ae642dd29005608318c4e5e18b3859b4035b3f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f2481d9ba170a7caa9b5a89bb0ae642dd29005608318c4e5e18b3859b4035b3f","first_computed_at":"2026-05-18T01:34:30.916795Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:34:30.916795Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"sea9mtziAJxDcPPugoD0V3dv6wMUwA7RTRWxiwpHcJdkpriCVkmMTwvcCbGYzWYXTiBAoWzkPWBmE29b2htNCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:34:30.917190Z","signed_message":"canonical_sha256_bytes"},"source_id":"1412.7941","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e2250a222d2cf2605eca010a81c3999baddf610157d7ae66c0d2f332f3eb0f9a","sha256:b07d20a8f3cb0d302aac8c2f38c89e953f6e39de879525cb7ae4241b9c54214a"],"state_sha256":"0bd81d59e2059f97d9c966d7725d8c890e89aaee703716acf47d67a2e9732415"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"tJlOKzZ4f2uS9c9bH99+n566ns4PMLv7d2ws+/NCTUZH9CKtcHERnBGBQwVx7mwaozzB9G83Z0IZVJdT0D7fDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T20:57:46.714258Z","bundle_sha256":"d9aad7daccded20c206cc0ff36ee1e6fe170c9e540bf7b0a36c90b07ad3ca54f"}}