{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:CYWBFWXPLSIYZGQ67I34JTMRQQ","short_pith_number":"pith:CYWBFWXP","canonical_record":{"source":{"id":"1510.04733","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-10-15T22:34:42Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"7d0fe4bb250eb9b5c667f52e0595b8d03c5a7f339549f1e3304fd079d1616249","abstract_canon_sha256":"c741413184a569afbf89d1c84268f36e03e942a0d19f38dbdcfbea4cba446b62"},"schema_version":"1.0"},"canonical_sha256":"162c12daef5c918c9a1efa37c4cd91841c375cb9e0a7e7a5f72d451f35a6b6d1","source":{"kind":"arxiv","id":"1510.04733","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.04733","created_at":"2026-05-18T01:12:43Z"},{"alias_kind":"arxiv_version","alias_value":"1510.04733v2","created_at":"2026-05-18T01:12:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.04733","created_at":"2026-05-18T01:12:43Z"},{"alias_kind":"pith_short_12","alias_value":"CYWBFWXPLSIY","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"CYWBFWXPLSIYZGQ6","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"CYWBFWXP","created_at":"2026-05-18T12:29:17Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:CYWBFWXPLSIYZGQ67I34JTMRQQ","target":"record","payload":{"canonical_record":{"source":{"id":"1510.04733","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-10-15T22:34:42Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"7d0fe4bb250eb9b5c667f52e0595b8d03c5a7f339549f1e3304fd079d1616249","abstract_canon_sha256":"c741413184a569afbf89d1c84268f36e03e942a0d19f38dbdcfbea4cba446b62"},"schema_version":"1.0"},"canonical_sha256":"162c12daef5c918c9a1efa37c4cd91841c375cb9e0a7e7a5f72d451f35a6b6d1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:43.382781Z","signature_b64":"ARt68Jla4buGShOSdD2TOf6vzGBhYQHjra2InZkcIhoPaAJfOAdmBUWRFCfbPBOiByHULMqThWgnSvlOeI+wCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"162c12daef5c918c9a1efa37c4cd91841c375cb9e0a7e7a5f72d451f35a6b6d1","last_reissued_at":"2026-05-18T01:12:43.382423Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:43.382423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1510.04733","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:12:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LLaUZcl33uQJxvu0GkYeRyM23FhFHViJlKAkAs1vb0agi/3qtKaEJvf2OIBETK+L2g5of9WnsFfA6MnutPFnCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T15:22:13.812228Z"},"content_sha256":"d358cdd62b3079a5060c5e23e089532a263bf29bf6f58d953262ab02866dd2f4","schema_version":"1.0","event_id":"sha256:d358cdd62b3079a5060c5e23e089532a263bf29bf6f58d953262ab02866dd2f4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:CYWBFWXPLSIYZGQ67I34JTMRQQ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Random hypersurfaces and embedding curves in surfaces over finite fields","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.NT","authors_text":"Joseph Gunther","submitted_at":"2015-10-15T22:34:42Z","abstract_excerpt":"We use Poonen's closed point sieve to prove two independent results. First, we show that the obvious obstruction to embedding a curve in a smooth surface is the only obstruction over a perfect field, by proving the finite field analogue of a Bertini-type result of Altman and Kleiman. Second, we prove a conjecture of Vakil and Wood on the asymptotic probability of hypersurface sections having a prescribed number of singularities."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04733","kind":"arxiv","version":2},"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":"2026-05-18T01:12:43Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F+TODKjYS+Epj15LBOCjXT2S8aEKF23tE0D4mMB7+pZn+3wx/bJB1Lv0ZJw3/MHpBflo2kaGwdrzgKaXdcp3DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T15:22:13.812579Z"},"content_sha256":"597c23a961dd9f9fc7f913899c5db7ec9d9199676d37c00076631e59b9374748","schema_version":"1.0","event_id":"sha256:597c23a961dd9f9fc7f913899c5db7ec9d9199676d37c00076631e59b9374748"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CYWBFWXPLSIYZGQ67I34JTMRQQ/bundle.json","state_url":"https://pith.science/pith/CYWBFWXPLSIYZGQ67I34JTMRQQ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CYWBFWXPLSIYZGQ67I34JTMRQQ/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":"2026-06-05T15:22:13Z","links":{"resolver":"https://pith.science/pith/CYWBFWXPLSIYZGQ67I34JTMRQQ","bundle":"https://pith.science/pith/CYWBFWXPLSIYZGQ67I34JTMRQQ/bundle.json","state":"https://pith.science/pith/CYWBFWXPLSIYZGQ67I34JTMRQQ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CYWBFWXPLSIYZGQ67I34JTMRQQ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:CYWBFWXPLSIYZGQ67I34JTMRQQ","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":"c741413184a569afbf89d1c84268f36e03e942a0d19f38dbdcfbea4cba446b62","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-10-15T22:34:42Z","title_canon_sha256":"7d0fe4bb250eb9b5c667f52e0595b8d03c5a7f339549f1e3304fd079d1616249"},"schema_version":"1.0","source":{"id":"1510.04733","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1510.04733","created_at":"2026-05-18T01:12:43Z"},{"alias_kind":"arxiv_version","alias_value":"1510.04733v2","created_at":"2026-05-18T01:12:43Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1510.04733","created_at":"2026-05-18T01:12:43Z"},{"alias_kind":"pith_short_12","alias_value":"CYWBFWXPLSIY","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_16","alias_value":"CYWBFWXPLSIYZGQ6","created_at":"2026-05-18T12:29:17Z"},{"alias_kind":"pith_short_8","alias_value":"CYWBFWXP","created_at":"2026-05-18T12:29:17Z"}],"graph_snapshots":[{"event_id":"sha256:597c23a961dd9f9fc7f913899c5db7ec9d9199676d37c00076631e59b9374748","target":"graph","created_at":"2026-05-18T01:12:43Z","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 use Poonen's closed point sieve to prove two independent results. First, we show that the obvious obstruction to embedding a curve in a smooth surface is the only obstruction over a perfect field, by proving the finite field analogue of a Bertini-type result of Altman and Kleiman. Second, we prove a conjecture of Vakil and Wood on the asymptotic probability of hypersurface sections having a prescribed number of singularities.","authors_text":"Joseph Gunther","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-10-15T22:34:42Z","title":"Random hypersurfaces and embedding curves in surfaces over finite fields"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.04733","kind":"arxiv","version":2},"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:d358cdd62b3079a5060c5e23e089532a263bf29bf6f58d953262ab02866dd2f4","target":"record","created_at":"2026-05-18T01:12:43Z","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":"c741413184a569afbf89d1c84268f36e03e942a0d19f38dbdcfbea4cba446b62","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2015-10-15T22:34:42Z","title_canon_sha256":"7d0fe4bb250eb9b5c667f52e0595b8d03c5a7f339549f1e3304fd079d1616249"},"schema_version":"1.0","source":{"id":"1510.04733","kind":"arxiv","version":2}},"canonical_sha256":"162c12daef5c918c9a1efa37c4cd91841c375cb9e0a7e7a5f72d451f35a6b6d1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"162c12daef5c918c9a1efa37c4cd91841c375cb9e0a7e7a5f72d451f35a6b6d1","first_computed_at":"2026-05-18T01:12:43.382423Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:12:43.382423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ARt68Jla4buGShOSdD2TOf6vzGBhYQHjra2InZkcIhoPaAJfOAdmBUWRFCfbPBOiByHULMqThWgnSvlOeI+wCw==","signature_status":"signed_v1","signed_at":"2026-05-18T01:12:43.382781Z","signed_message":"canonical_sha256_bytes"},"source_id":"1510.04733","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:d358cdd62b3079a5060c5e23e089532a263bf29bf6f58d953262ab02866dd2f4","sha256:597c23a961dd9f9fc7f913899c5db7ec9d9199676d37c00076631e59b9374748"],"state_sha256":"8e2b55941442a09a37c1c74446b72a9dd4011d91045dbaeda54e9a57051354d2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cPPr2AJ6uVhNFl+GKYL9fTQ8rRTyK3w98YPViKBJhKP8DFtwzlN+Pmf4NGWKmRehKHEvgGto/ZIgCVHWTdBtCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T15:22:13.814623Z","bundle_sha256":"c7e7c456ccd301fcd1499833558005bd5a5ecdef6f062b2cede333070d664b62"}}