{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7UDYIGUP46CDGC3QNMVTK7TSPA","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":"4d76798ffdd0017d91413c2ec09e6f4934bd057d2d0680fe233f1a4c6dda626c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-10-17T07:31:44Z","title_canon_sha256":"20f8f32013dd73b0578df85a3dd43eed60a86bc03d95e08012a469de54d4612e"},"schema_version":"1.0","source":{"id":"1110.3589","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.3589","created_at":"2026-05-18T03:49:22Z"},{"alias_kind":"arxiv_version","alias_value":"1110.3589v1","created_at":"2026-05-18T03:49:22Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.3589","created_at":"2026-05-18T03:49:22Z"},{"alias_kind":"pith_short_12","alias_value":"7UDYIGUP46CD","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7UDYIGUP46CDGC3Q","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7UDYIGUP","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:fdfda3634f577577cac86683b20c5eca0339b5da120c82c6c84d6cac84a3707d","target":"graph","created_at":"2026-05-18T03:49:22Z","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":"Let $f(x,y)=0$ and $l(x,y)=0$ be respectively a singular and a regular analytic curve defined in the neighborhood of the origin of the complex plane. We study the family of analytic curves $f(x,y)-tl(x,y)^M=0$, where $t$ is a complex parameter. For all but a finite number of parameters the curves of this family have the same embedded topological type. The exceptional parameters are called special values.\n  We show that the number of nonzero special values does not exceed the number of components of the curve $f(x,y)=0$ counted without multiplicities. Then we apply this result to estimate the n","authors_text":"Janusz Gwozdziewicz","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-10-17T07:31:44Z","title":"Ephraim's Pencils"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3589","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":"sha256:49881e89b36341837e5b51b2f20ea8322298b6fafd616f4b2c65bdda843969e6","target":"record","created_at":"2026-05-18T03:49:22Z","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":"4d76798ffdd0017d91413c2ec09e6f4934bd057d2d0680fe233f1a4c6dda626c","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2011-10-17T07:31:44Z","title_canon_sha256":"20f8f32013dd73b0578df85a3dd43eed60a86bc03d95e08012a469de54d4612e"},"schema_version":"1.0","source":{"id":"1110.3589","kind":"arxiv","version":1}},"canonical_sha256":"fd07841a8fe784330b706b2b357e7278178137555dfcec208747713c0f7645ea","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fd07841a8fe784330b706b2b357e7278178137555dfcec208747713c0f7645ea","first_computed_at":"2026-05-18T03:49:22.158300Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:49:22.158300Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"61ib9Qoc3I+EPA3WsngCMf4nblLQSczDYkBOd01bnFH9UldPedV8jFRuveDhIcn41QQ2etXNsfDfF5vtJ7HSAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:49:22.159066Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.3589","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:49881e89b36341837e5b51b2f20ea8322298b6fafd616f4b2c65bdda843969e6","sha256:fdfda3634f577577cac86683b20c5eca0339b5da120c82c6c84d6cac84a3707d"],"state_sha256":"5fb7dc8d1d000dddc7399c8fdfe2d0e494b6adc21e918545ff54c6846b392cf5"}