{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:WR2NJLZEOQCXGZIBQHSDVWNHIP","short_pith_number":"pith:WR2NJLZE","canonical_record":{"source":{"id":"1404.7704","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-04-30T12:52:42Z","cross_cats_sorted":[],"title_canon_sha256":"d99781444d120b88dfc475aee4e35502f67245ddc5df7284d9e7dec484f30c4d","abstract_canon_sha256":"7901b87d5cb3e0bbf9fa174bc50706290e9aa5875053073a0a34c172bcf1fb07"},"schema_version":"1.0"},"canonical_sha256":"b474d4af24740573650181e43ad9a743d87d61df00ef4e47b21b8a2ce1651830","source":{"kind":"arxiv","id":"1404.7704","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.7704","created_at":"2026-05-18T00:58:41Z"},{"alias_kind":"arxiv_version","alias_value":"1404.7704v2","created_at":"2026-05-18T00:58:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.7704","created_at":"2026-05-18T00:58:41Z"},{"alias_kind":"pith_short_12","alias_value":"WR2NJLZEOQCX","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WR2NJLZEOQCXGZIB","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WR2NJLZE","created_at":"2026-05-18T12:28:54Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:WR2NJLZEOQCXGZIBQHSDVWNHIP","target":"record","payload":{"canonical_record":{"source":{"id":"1404.7704","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-04-30T12:52:42Z","cross_cats_sorted":[],"title_canon_sha256":"d99781444d120b88dfc475aee4e35502f67245ddc5df7284d9e7dec484f30c4d","abstract_canon_sha256":"7901b87d5cb3e0bbf9fa174bc50706290e9aa5875053073a0a34c172bcf1fb07"},"schema_version":"1.0"},"canonical_sha256":"b474d4af24740573650181e43ad9a743d87d61df00ef4e47b21b8a2ce1651830","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:58:41.547219Z","signature_b64":"zzUkRehrMAnqqy+IebaxAUHAkunDjvPzLATiT/9/Au1WqtoeTYB4SCf/jZ6qM/QiFFgjj+4uoHBmIQAbdP2TAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b474d4af24740573650181e43ad9a743d87d61df00ef4e47b21b8a2ce1651830","last_reissued_at":"2026-05-18T00:58:41.546572Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:58:41.546572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1404.7704","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":"2026-05-18T00:58:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"sZvJw5Giy82pYbgtfMzCId0snTdoIj+YBP7eTlnkqv9TRztA7C/5O71itZktPDtXKUGbg/Et4VSEVfD+BflkBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T20:55:29.197766Z"},"content_sha256":"9e4fe5840930293c88663b1a565ce0dd746aedd6a48f99515cda9f9fbb6642e5","schema_version":"1.0","event_id":"sha256:9e4fe5840930293c88663b1a565ce0dd746aedd6a48f99515cda9f9fbb6642e5"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:WR2NJLZEOQCXGZIBQHSDVWNHIP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Milnor numbers in deformations of homogeneous singularities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Justyna Walewska, Szymon Brzostowski, Tadeusz Krasinski","submitted_at":"2014-04-30T12:52:42Z","abstract_excerpt":"Let f_0 be a plane curve singularity. We study the Minor numbers of singularities in deformations of f_0. We completely describe the set of these Milnor numbers for homogeneous singularities f_0 in the case of non-degenerate deformations and obtain some partial results on this set in the general case."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.7704","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":"2026-05-18T00:58:41Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"GcJw0WBsypZGG4pIiBGths7m/OuFxBbVdozKUGPwskpWD0qJQuphSq1n+3sN4e0xYk/9coV5FG6ISXZWfPdoCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T20:55:29.198481Z"},"content_sha256":"459e6dca4dde7f08688f89fcfaa72de27f87437ce6c3d92176a6fcc21b1d08a0","schema_version":"1.0","event_id":"sha256:459e6dca4dde7f08688f89fcfaa72de27f87437ce6c3d92176a6fcc21b1d08a0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WR2NJLZEOQCXGZIBQHSDVWNHIP/bundle.json","state_url":"https://pith.science/pith/WR2NJLZEOQCXGZIBQHSDVWNHIP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WR2NJLZEOQCXGZIBQHSDVWNHIP/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":"2026-06-08T20:55:29Z","links":{"resolver":"https://pith.science/pith/WR2NJLZEOQCXGZIBQHSDVWNHIP","bundle":"https://pith.science/pith/WR2NJLZEOQCXGZIBQHSDVWNHIP/bundle.json","state":"https://pith.science/pith/WR2NJLZEOQCXGZIBQHSDVWNHIP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WR2NJLZEOQCXGZIBQHSDVWNHIP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:WR2NJLZEOQCXGZIBQHSDVWNHIP","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":"7901b87d5cb3e0bbf9fa174bc50706290e9aa5875053073a0a34c172bcf1fb07","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-04-30T12:52:42Z","title_canon_sha256":"d99781444d120b88dfc475aee4e35502f67245ddc5df7284d9e7dec484f30c4d"},"schema_version":"1.0","source":{"id":"1404.7704","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.7704","created_at":"2026-05-18T00:58:41Z"},{"alias_kind":"arxiv_version","alias_value":"1404.7704v2","created_at":"2026-05-18T00:58:41Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.7704","created_at":"2026-05-18T00:58:41Z"},{"alias_kind":"pith_short_12","alias_value":"WR2NJLZEOQCX","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"WR2NJLZEOQCXGZIB","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"WR2NJLZE","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:459e6dca4dde7f08688f89fcfaa72de27f87437ce6c3d92176a6fcc21b1d08a0","target":"graph","created_at":"2026-05-18T00:58:41Z","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_0 be a plane curve singularity. We study the Minor numbers of singularities in deformations of f_0. We completely describe the set of these Milnor numbers for homogeneous singularities f_0 in the case of non-degenerate deformations and obtain some partial results on this set in the general case.","authors_text":"Justyna Walewska, Szymon Brzostowski, Tadeusz Krasinski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-04-30T12:52:42Z","title":"Milnor numbers in deformations of homogeneous singularities"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.7704","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":"sha256:9e4fe5840930293c88663b1a565ce0dd746aedd6a48f99515cda9f9fbb6642e5","target":"record","created_at":"2026-05-18T00:58:41Z","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":"7901b87d5cb3e0bbf9fa174bc50706290e9aa5875053073a0a34c172bcf1fb07","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AG","submitted_at":"2014-04-30T12:52:42Z","title_canon_sha256":"d99781444d120b88dfc475aee4e35502f67245ddc5df7284d9e7dec484f30c4d"},"schema_version":"1.0","source":{"id":"1404.7704","kind":"arxiv","version":2}},"canonical_sha256":"b474d4af24740573650181e43ad9a743d87d61df00ef4e47b21b8a2ce1651830","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b474d4af24740573650181e43ad9a743d87d61df00ef4e47b21b8a2ce1651830","first_computed_at":"2026-05-18T00:58:41.546572Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:58:41.546572Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"zzUkRehrMAnqqy+IebaxAUHAkunDjvPzLATiT/9/Au1WqtoeTYB4SCf/jZ6qM/QiFFgjj+4uoHBmIQAbdP2TAw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:58:41.547219Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.7704","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e4fe5840930293c88663b1a565ce0dd746aedd6a48f99515cda9f9fbb6642e5","sha256:459e6dca4dde7f08688f89fcfaa72de27f87437ce6c3d92176a6fcc21b1d08a0"],"state_sha256":"7cb534bff8f42d9181822716ef56d8ce22e2120f239ff1a9fe1c6d7849a06313"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"J7AgyfZ34fcWH31lwZcBY2V4XUwiKe4i0qyRsYE4z1gyD5iCOp8csQAOC9gdVe+r/iUOZnWBkznmKuwvlYJBCA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T20:55:29.203225Z","bundle_sha256":"fa00d903e9ab4cb28d849605a0defa99311770e4b4f164572c69fb2ffd2b1273"}}