{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2007:47NFY3OCA36CWKUZIU5HOWH5HP","short_pith_number":"pith:47NFY3OC","canonical_record":{"source":{"id":"0710.5279","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-10-28T12:42:36Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"63209a2a18b4eb5ef82bff8b42da0b613f9c9a19537afebcb4742fd2ed19b4b6","abstract_canon_sha256":"ffee1b25147b15d16fb784d6c5b396271ac946018f25058035c925591dc6b522"},"schema_version":"1.0"},"canonical_sha256":"e7da5c6dc206fc2b2a99453a7758fd3beeb97f3addd786fe1e9cee9cd536672b","source":{"kind":"arxiv","id":"0710.5279","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.5279","created_at":"2026-05-18T03:05:55Z"},{"alias_kind":"arxiv_version","alias_value":"0710.5279v3","created_at":"2026-05-18T03:05:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.5279","created_at":"2026-05-18T03:05:55Z"},{"alias_kind":"pith_short_12","alias_value":"47NFY3OCA36C","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"47NFY3OCA36CWKUZ","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"47NFY3OC","created_at":"2026-05-18T12:25:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2007:47NFY3OCA36CWKUZIU5HOWH5HP","target":"record","payload":{"canonical_record":{"source":{"id":"0710.5279","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-10-28T12:42:36Z","cross_cats_sorted":["math.GR"],"title_canon_sha256":"63209a2a18b4eb5ef82bff8b42da0b613f9c9a19537afebcb4742fd2ed19b4b6","abstract_canon_sha256":"ffee1b25147b15d16fb784d6c5b396271ac946018f25058035c925591dc6b522"},"schema_version":"1.0"},"canonical_sha256":"e7da5c6dc206fc2b2a99453a7758fd3beeb97f3addd786fe1e9cee9cd536672b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:55.544895Z","signature_b64":"7Wyldwz9CdsZjYjqtFPd9r9H/gvdCOPxj2Ljt1HlT5ReQsGJziPfe5c8lZvMq5ATVgnsGLSpkTzu1DpVwxydDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e7da5c6dc206fc2b2a99453a7758fd3beeb97f3addd786fe1e9cee9cd536672b","last_reissued_at":"2026-05-18T03:05:55.544208Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:55.544208Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"0710.5279","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":"2026-05-18T03:05:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IEBouuJPwDVYmvac8OBsGRPHqE97b0nJYzolVyI5XZkb8rRd0OO89y56nt7e7zYjHhugT2Hog3V6k3Fuxb34Bg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:28:27.211575Z"},"content_sha256":"633908c7cf4fcb483bec4fcfafe54de593671c29d8a8f6e278509a2f242bfdc0","schema_version":"1.0","event_id":"sha256:633908c7cf4fcb483bec4fcfafe54de593671c29d8a8f6e278509a2f242bfdc0"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2007:47NFY3OCA36CWKUZIU5HOWH5HP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Normal subgroups of the algebraic fundamental group of affine curves in positive characteristic","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.AG","authors_text":"Amilcar Pacheco, Katherine F. Stevenson, Pavel Zalesski","submitted_at":"2007-10-28T12:42:36Z","abstract_excerpt":"Let $\\pi_1(C)$ be the algebraic fundamental group of a smooth connected affine curve, defined over an algebraically closed field of characteristic $p>0$ of countable cardinality. Let $N$ be a normal (resp. characteristic) subgroup of $\\pi_1(C)$. Under the hypothesis that the quotient $\\pi_1(C)/N$ admits an infinitely generated Sylow $p$-subgroup, we prove that $N$ is indeed isomorphic to a normal (resp. characteristic) subgroup of a free profinite group of countable cardinality. As a consequence, every proper open subgroup of $N$ is a free profinite group of countable cardinality."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.5279","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":"2026-05-18T03:05:55Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5vEw9zSr34mGm3B68cLUpXJ5KVgXkpaLcYDR/AaBbGe9tAmB1mBH0f2LpfxiJc5Uz/MQzsGiqQSJ8nG6CDS8AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T16:28:27.212201Z"},"content_sha256":"5d8635227d172b795224537cbc2a54758070db7ff92fb59e0ce02b969d581cbb","schema_version":"1.0","event_id":"sha256:5d8635227d172b795224537cbc2a54758070db7ff92fb59e0ce02b969d581cbb"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/47NFY3OCA36CWKUZIU5HOWH5HP/bundle.json","state_url":"https://pith.science/pith/47NFY3OCA36CWKUZIU5HOWH5HP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/47NFY3OCA36CWKUZIU5HOWH5HP/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":"2026-06-06T16:28:27Z","links":{"resolver":"https://pith.science/pith/47NFY3OCA36CWKUZIU5HOWH5HP","bundle":"https://pith.science/pith/47NFY3OCA36CWKUZIU5HOWH5HP/bundle.json","state":"https://pith.science/pith/47NFY3OCA36CWKUZIU5HOWH5HP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/47NFY3OCA36CWKUZIU5HOWH5HP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2007:47NFY3OCA36CWKUZIU5HOWH5HP","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":"ffee1b25147b15d16fb784d6c5b396271ac946018f25058035c925591dc6b522","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-10-28T12:42:36Z","title_canon_sha256":"63209a2a18b4eb5ef82bff8b42da0b613f9c9a19537afebcb4742fd2ed19b4b6"},"schema_version":"1.0","source":{"id":"0710.5279","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0710.5279","created_at":"2026-05-18T03:05:55Z"},{"alias_kind":"arxiv_version","alias_value":"0710.5279v3","created_at":"2026-05-18T03:05:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0710.5279","created_at":"2026-05-18T03:05:55Z"},{"alias_kind":"pith_short_12","alias_value":"47NFY3OCA36C","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"47NFY3OCA36CWKUZ","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"47NFY3OC","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:5d8635227d172b795224537cbc2a54758070db7ff92fb59e0ce02b969d581cbb","target":"graph","created_at":"2026-05-18T03:05:55Z","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":"Let $\\pi_1(C)$ be the algebraic fundamental group of a smooth connected affine curve, defined over an algebraically closed field of characteristic $p>0$ of countable cardinality. Let $N$ be a normal (resp. characteristic) subgroup of $\\pi_1(C)$. Under the hypothesis that the quotient $\\pi_1(C)/N$ admits an infinitely generated Sylow $p$-subgroup, we prove that $N$ is indeed isomorphic to a normal (resp. characteristic) subgroup of a free profinite group of countable cardinality. As a consequence, every proper open subgroup of $N$ is a free profinite group of countable cardinality.","authors_text":"Amilcar Pacheco, Katherine F. Stevenson, Pavel Zalesski","cross_cats":["math.GR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-10-28T12:42:36Z","title":"Normal subgroups of the algebraic fundamental group of affine curves in positive characteristic"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0710.5279","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":"sha256:633908c7cf4fcb483bec4fcfafe54de593671c29d8a8f6e278509a2f242bfdc0","target":"record","created_at":"2026-05-18T03:05:55Z","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":"ffee1b25147b15d16fb784d6c5b396271ac946018f25058035c925591dc6b522","cross_cats_sorted":["math.GR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2007-10-28T12:42:36Z","title_canon_sha256":"63209a2a18b4eb5ef82bff8b42da0b613f9c9a19537afebcb4742fd2ed19b4b6"},"schema_version":"1.0","source":{"id":"0710.5279","kind":"arxiv","version":3}},"canonical_sha256":"e7da5c6dc206fc2b2a99453a7758fd3beeb97f3addd786fe1e9cee9cd536672b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e7da5c6dc206fc2b2a99453a7758fd3beeb97f3addd786fe1e9cee9cd536672b","first_computed_at":"2026-05-18T03:05:55.544208Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:55.544208Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7Wyldwz9CdsZjYjqtFPd9r9H/gvdCOPxj2Ljt1HlT5ReQsGJziPfe5c8lZvMq5ATVgnsGLSpkTzu1DpVwxydDg==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:55.544895Z","signed_message":"canonical_sha256_bytes"},"source_id":"0710.5279","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:633908c7cf4fcb483bec4fcfafe54de593671c29d8a8f6e278509a2f242bfdc0","sha256:5d8635227d172b795224537cbc2a54758070db7ff92fb59e0ce02b969d581cbb"],"state_sha256":"7a98a61b4f6098e80e106bb14b30c680dfabbb60d01c174df3a1d3e5071e4da8"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+uDdHdw1wd9Oa2IyAPOwIt+3z9IZQ+WI10OUDcbTyoFtl4flpQCuw/BFsnemaDVVnzDevRJDTdLpaUV6C0wWAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T16:28:27.215539Z","bundle_sha256":"f5e549e5ce87397527a77881ea495999b0b70da8c0d9ce3cf7caf38fb5c70792"}}