{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2012:K52L4CQRCM565VUIEJEO5O3J3U","short_pith_number":"pith:K52L4CQR","canonical_record":{"source":{"id":"1201.6579","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-01-31T15:41:20Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"c74408c3cdc5e476b314cf1408c81ef7d195719b8eafb27c3c02203e6fb0e9ca","abstract_canon_sha256":"ef697af917f563ac38b85cb92211fcb5c12082d3078416e541efb864f475bfe6"},"schema_version":"1.0"},"canonical_sha256":"5774be0a11133beed6882248eebb69dd1ffa4aff97c3444b502172bf2496a39a","source":{"kind":"arxiv","id":"1201.6579","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.6579","created_at":"2026-05-18T02:28:48Z"},{"alias_kind":"arxiv_version","alias_value":"1201.6579v1","created_at":"2026-05-18T02:28:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.6579","created_at":"2026-05-18T02:28:48Z"},{"alias_kind":"pith_short_12","alias_value":"K52L4CQRCM56","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"K52L4CQRCM565VUI","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"K52L4CQR","created_at":"2026-05-18T12:27:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2012:K52L4CQRCM565VUIEJEO5O3J3U","target":"record","payload":{"canonical_record":{"source":{"id":"1201.6579","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-01-31T15:41:20Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"c74408c3cdc5e476b314cf1408c81ef7d195719b8eafb27c3c02203e6fb0e9ca","abstract_canon_sha256":"ef697af917f563ac38b85cb92211fcb5c12082d3078416e541efb864f475bfe6"},"schema_version":"1.0"},"canonical_sha256":"5774be0a11133beed6882248eebb69dd1ffa4aff97c3444b502172bf2496a39a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:28:48.514942Z","signature_b64":"9uozkc+m9qbkIGMhFrQT83IcZ6fzl1U3XodIIS53tnrKIzkc0GNRbCJgo3yOS1XR6rYS/lSZfvurKmFJEYAlBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5774be0a11133beed6882248eebb69dd1ffa4aff97c3444b502172bf2496a39a","last_reissued_at":"2026-05-18T02:28:48.514561Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:28:48.514561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1201.6579","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":"2026-05-18T02:28:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"54gsaCzKGZYEfOuHjupTQaD0jcGKksSaibP6FJYTbAvHrIfWLyrn0s5GPlW5LJTp/edy2TjY+/uznP4d30wcAw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T13:07:10.115446Z"},"content_sha256":"ac66ea817e2de1ac9a01c65c2c6e429ba4c06b60423264e4693b60deb3306538","schema_version":"1.0","event_id":"sha256:ac66ea817e2de1ac9a01c65c2c6e429ba4c06b60423264e4693b60deb3306538"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2012:K52L4CQRCM565VUIEJEO5O3J3U","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"One branch curve singularities with at most 2-parameter families of ideals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.AC","authors_text":"Ruslan V. Skuratovskii, Yuriy A. Drozd","submitted_at":"2012-01-31T15:41:20Z","abstract_excerpt":"A criterion is given in order that the ideals of a one branch curve singularity form at most 2-parameter families. Namely, we present a list of plane curve singularities from the Arnold's classification which are the smallest among all one branch singularities having at most 2-parameter families of ideals."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.6579","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":"2026-05-18T02:28:48Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q5qlRuXsc0y9ecxacbsY0ZvM6X3ohu4qFMTXdetzH15bk0jbzydZP0cnv7HF98vDk1r8S1/u7o3b7DBt/i+/Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T13:07:10.116110Z"},"content_sha256":"c58d5bb9334011d1a8804bbd637b29c3252f21195f974de0ddcbf17fbee80b5d","schema_version":"1.0","event_id":"sha256:c58d5bb9334011d1a8804bbd637b29c3252f21195f974de0ddcbf17fbee80b5d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/K52L4CQRCM565VUIEJEO5O3J3U/bundle.json","state_url":"https://pith.science/pith/K52L4CQRCM565VUIEJEO5O3J3U/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/K52L4CQRCM565VUIEJEO5O3J3U/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":"2026-05-31T13:07:10Z","links":{"resolver":"https://pith.science/pith/K52L4CQRCM565VUIEJEO5O3J3U","bundle":"https://pith.science/pith/K52L4CQRCM565VUIEJEO5O3J3U/bundle.json","state":"https://pith.science/pith/K52L4CQRCM565VUIEJEO5O3J3U/state.json","well_known_bundle":"https://pith.science/.well-known/pith/K52L4CQRCM565VUIEJEO5O3J3U/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:K52L4CQRCM565VUIEJEO5O3J3U","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":"ef697af917f563ac38b85cb92211fcb5c12082d3078416e541efb864f475bfe6","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-01-31T15:41:20Z","title_canon_sha256":"c74408c3cdc5e476b314cf1408c81ef7d195719b8eafb27c3c02203e6fb0e9ca"},"schema_version":"1.0","source":{"id":"1201.6579","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1201.6579","created_at":"2026-05-18T02:28:48Z"},{"alias_kind":"arxiv_version","alias_value":"1201.6579v1","created_at":"2026-05-18T02:28:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1201.6579","created_at":"2026-05-18T02:28:48Z"},{"alias_kind":"pith_short_12","alias_value":"K52L4CQRCM56","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_16","alias_value":"K52L4CQRCM565VUI","created_at":"2026-05-18T12:27:11Z"},{"alias_kind":"pith_short_8","alias_value":"K52L4CQR","created_at":"2026-05-18T12:27:11Z"}],"graph_snapshots":[{"event_id":"sha256:c58d5bb9334011d1a8804bbd637b29c3252f21195f974de0ddcbf17fbee80b5d","target":"graph","created_at":"2026-05-18T02:28:48Z","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":"A criterion is given in order that the ideals of a one branch curve singularity form at most 2-parameter families. Namely, we present a list of plane curve singularities from the Arnold's classification which are the smallest among all one branch singularities having at most 2-parameter families of ideals.","authors_text":"Ruslan V. Skuratovskii, Yuriy A. Drozd","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-01-31T15:41:20Z","title":"One branch curve singularities with at most 2-parameter families of ideals"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1201.6579","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:ac66ea817e2de1ac9a01c65c2c6e429ba4c06b60423264e4693b60deb3306538","target":"record","created_at":"2026-05-18T02:28:48Z","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":"ef697af917f563ac38b85cb92211fcb5c12082d3078416e541efb864f475bfe6","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AC","submitted_at":"2012-01-31T15:41:20Z","title_canon_sha256":"c74408c3cdc5e476b314cf1408c81ef7d195719b8eafb27c3c02203e6fb0e9ca"},"schema_version":"1.0","source":{"id":"1201.6579","kind":"arxiv","version":1}},"canonical_sha256":"5774be0a11133beed6882248eebb69dd1ffa4aff97c3444b502172bf2496a39a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5774be0a11133beed6882248eebb69dd1ffa4aff97c3444b502172bf2496a39a","first_computed_at":"2026-05-18T02:28:48.514561Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:28:48.514561Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"9uozkc+m9qbkIGMhFrQT83IcZ6fzl1U3XodIIS53tnrKIzkc0GNRbCJgo3yOS1XR6rYS/lSZfvurKmFJEYAlBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:28:48.514942Z","signed_message":"canonical_sha256_bytes"},"source_id":"1201.6579","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ac66ea817e2de1ac9a01c65c2c6e429ba4c06b60423264e4693b60deb3306538","sha256:c58d5bb9334011d1a8804bbd637b29c3252f21195f974de0ddcbf17fbee80b5d"],"state_sha256":"a38593107d740adbffb9523a5c897c5fb456399da16f8570c4b57b5f8b352f66"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"52sM3O/rTe9oV2PqO9O3+feFBFZW72eoymQgX+9VDzvFD1g8JFCAjPL4JrfFjOj3aMPsTTuXnUxu5auw+pKJBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T13:07:10.119923Z","bundle_sha256":"fbbc382da32562791e4cad09cc2c4256713c58c08b2dcfd17454d61a10de7248"}}