{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:NY7YX53M6OXDWWBMFDJNLD754B","short_pith_number":"pith:NY7YX53M","canonical_record":{"source":{"id":"1510.06874","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-10-23T09:53:02Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"1e0f5a6f3de7aeaf36069ade256324f7af6e3d3eec0e75bdf2a20a841fb85658","abstract_canon_sha256":"7a4327f83f1b0a0434519bdc71e38ecbb4a3dfb89e6a92c36954f3f5ccaa7624"},"schema_version":"1.0"},"canonical_sha256":"6e3f8bf76cf3ae3b582c28d2d58ffde0642058dc48c4deba317a6aef2b05409e","source":{"kind":"arxiv","id":"1510.06874","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.06874","created_at":"2026-05-18T01:29:22Z"},{"alias_kind":"arxiv_version","alias_value":"1510.06874v1","created_at":"2026-05-18T01:29:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.06874","created_at":"2026-05-18T01:29:22Z"},{"alias_kind":"pith_short_12","alias_value":"NY7YX53M6OXD","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"NY7YX53M6OXDWWBM","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"NY7YX53M","created_at":"2026-05-18T12:29:34Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:NY7YX53M6OXDWWBMFDJNLD754B","target":"record","payload":{"canonical_record":{"source":{"id":"1510.06874","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-10-23T09:53:02Z","cross_cats_sorted":["math.NT"],"title_canon_sha256":"1e0f5a6f3de7aeaf36069ade256324f7af6e3d3eec0e75bdf2a20a841fb85658","abstract_canon_sha256":"7a4327f83f1b0a0434519bdc71e38ecbb4a3dfb89e6a92c36954f3f5ccaa7624"},"schema_version":"1.0"},"canonical_sha256":"6e3f8bf76cf3ae3b582c28d2d58ffde0642058dc48c4deba317a6aef2b05409e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:29:22.848909Z","signature_b64":"ra8X2NCQoEi4rMWKCGgLijQHvXBzh/dwTpdH0HwjbyQZxdDqZuMbdzwc7Ocpp+fmeubt7Npf0eEOLXaZo5diCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6e3f8bf76cf3ae3b582c28d2d58ffde0642058dc48c4deba317a6aef2b05409e","last_reissued_at":"2026-05-18T01:29:22.848383Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:29:22.848383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.06874","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":"2026-05-18T01:29:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"nrUokSoJqBy7g0h387nrSkI1HsJU8+AxBIKpYKqx6QSXqSc0LvzRG4qu0BSpcbR6rinObISm6BfRtQQmqF67AA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T05:24:04.276639Z"},"content_sha256":"7e48c61b0609ecf7ec69580a0a4b5ad10f0537decc61564116fe4a371ae5f189","schema_version":"1.0","event_id":"sha256:7e48c61b0609ecf7ec69580a0a4b5ad10f0537decc61564116fe4a371ae5f189"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:NY7YX53M6OXDWWBMFDJNLD754B","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the existence of a torsor structure for Galois covers over a complete discrete valuation ring","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.AG","authors_text":"Mohamed saidi, Nicholas Williams","submitted_at":"2015-10-23T09:53:02Z","abstract_excerpt":"In this note we investigate the problem of existence of a torsor structure for Galois covers of (formal) schemes over a complete discrete valuation ring of residue characteristic $p>0$ in the case of abelian Galois groups of type (p,p,...,p)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.06874","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":"2026-05-18T01:29:22Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x31LO6tFpk5bPZZlfmst43MKswSlCzpVUQj2UcQpG0NlyC+2ItROrPgFM30hc6uUmKIvo/85Nd21FL/0bw31BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-26T05:24:04.276988Z"},"content_sha256":"f716fd939dd26cc50ed16691b3f2f08c8c2c9eb50752ef16c3ed52cde3192657","schema_version":"1.0","event_id":"sha256:f716fd939dd26cc50ed16691b3f2f08c8c2c9eb50752ef16c3ed52cde3192657"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/NY7YX53M6OXDWWBMFDJNLD754B/bundle.json","state_url":"https://pith.science/pith/NY7YX53M6OXDWWBMFDJNLD754B/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/NY7YX53M6OXDWWBMFDJNLD754B/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":"2026-06-26T05:24:04Z","links":{"resolver":"https://pith.science/pith/NY7YX53M6OXDWWBMFDJNLD754B","bundle":"https://pith.science/pith/NY7YX53M6OXDWWBMFDJNLD754B/bundle.json","state":"https://pith.science/pith/NY7YX53M6OXDWWBMFDJNLD754B/state.json","well_known_bundle":"https://pith.science/.well-known/pith/NY7YX53M6OXDWWBMFDJNLD754B/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:NY7YX53M6OXDWWBMFDJNLD754B","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":"7a4327f83f1b0a0434519bdc71e38ecbb4a3dfb89e6a92c36954f3f5ccaa7624","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-10-23T09:53:02Z","title_canon_sha256":"1e0f5a6f3de7aeaf36069ade256324f7af6e3d3eec0e75bdf2a20a841fb85658"},"schema_version":"1.0","source":{"id":"1510.06874","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.06874","created_at":"2026-05-18T01:29:22Z"},{"alias_kind":"arxiv_version","alias_value":"1510.06874v1","created_at":"2026-05-18T01:29:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.06874","created_at":"2026-05-18T01:29:22Z"},{"alias_kind":"pith_short_12","alias_value":"NY7YX53M6OXD","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_16","alias_value":"NY7YX53M6OXDWWBM","created_at":"2026-05-18T12:29:34Z"},{"alias_kind":"pith_short_8","alias_value":"NY7YX53M","created_at":"2026-05-18T12:29:34Z"}],"graph_snapshots":[{"event_id":"sha256:f716fd939dd26cc50ed16691b3f2f08c8c2c9eb50752ef16c3ed52cde3192657","target":"graph","created_at":"2026-05-18T01:29:22Z","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 note we investigate the problem of existence of a torsor structure for Galois covers of (formal) schemes over a complete discrete valuation ring of residue characteristic $p>0$ in the case of abelian Galois groups of type (p,p,...,p).","authors_text":"Mohamed saidi, Nicholas Williams","cross_cats":["math.NT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-10-23T09:53:02Z","title":"On the existence of a torsor structure for Galois covers over a complete discrete valuation ring"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.06874","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":"sha256:7e48c61b0609ecf7ec69580a0a4b5ad10f0537decc61564116fe4a371ae5f189","target":"record","created_at":"2026-05-18T01:29:22Z","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":"7a4327f83f1b0a0434519bdc71e38ecbb4a3dfb89e6a92c36954f3f5ccaa7624","cross_cats_sorted":["math.NT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2015-10-23T09:53:02Z","title_canon_sha256":"1e0f5a6f3de7aeaf36069ade256324f7af6e3d3eec0e75bdf2a20a841fb85658"},"schema_version":"1.0","source":{"id":"1510.06874","kind":"arxiv","version":1}},"canonical_sha256":"6e3f8bf76cf3ae3b582c28d2d58ffde0642058dc48c4deba317a6aef2b05409e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6e3f8bf76cf3ae3b582c28d2d58ffde0642058dc48c4deba317a6aef2b05409e","first_computed_at":"2026-05-18T01:29:22.848383Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:29:22.848383Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ra8X2NCQoEi4rMWKCGgLijQHvXBzh/dwTpdH0HwjbyQZxdDqZuMbdzwc7Ocpp+fmeubt7Npf0eEOLXaZo5diCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T01:29:22.848909Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.06874","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:7e48c61b0609ecf7ec69580a0a4b5ad10f0537decc61564116fe4a371ae5f189","sha256:f716fd939dd26cc50ed16691b3f2f08c8c2c9eb50752ef16c3ed52cde3192657"],"state_sha256":"b9773445ddb8655a5f190343aaad195702bf7dfcd9e8b880e26e983638b57ba9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+xLa8z3iJhyX5jtBWv6R6Br92Bot7nrEZtMBUAOXlMEpgOk+FIlYnvkrQpRJuuqMKr6673ZETNX5EdJSiBSXBw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-26T05:24:04.278966Z","bundle_sha256":"635e28817a5ffca2652c5b0bd22171e97e12b066cf37ac533c51eff086ac2582"}}