{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:4PPXZX67X4E77YYBB345HWL5PE","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":"da091df5c2825250fc98c7b0c72a76423d5eb709b211955dec5a1c0bc150b3f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-03-20T21:34:23Z","title_canon_sha256":"96f21e9fd1a61c5648515b0cc38df6b95400f5374949c3ecfd82ab15b855e3f4"},"schema_version":"1.0","source":{"id":"1103.3891","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1103.3891","created_at":"2026-05-18T03:21:32Z"},{"alias_kind":"arxiv_version","alias_value":"1103.3891v1","created_at":"2026-05-18T03:21:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1103.3891","created_at":"2026-05-18T03:21:32Z"},{"alias_kind":"pith_short_12","alias_value":"4PPXZX67X4E7","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_16","alias_value":"4PPXZX67X4E77YYB","created_at":"2026-05-18T12:26:20Z"},{"alias_kind":"pith_short_8","alias_value":"4PPXZX67","created_at":"2026-05-18T12:26:20Z"}],"graph_snapshots":[{"event_id":"sha256:70d06480c4fe4da19442b835f454740d388e4021d15d3bddaca2932cd22c7977","target":"graph","created_at":"2026-05-18T03:21:32Z","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 generalize recent developments on normal forms and the spectral sequences method to make a foundation for parametric normal forms. We further introduce a new style and costyle to obtain unique parametric normal forms. The results are applied to systems of generalized Hopf singularity with multiple parameters. A different (new) version of this paper has been submitted for a possible publication in a refereed journal.","authors_text":"Majid Gazor, Pei Yu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-03-20T21:34:23Z","title":"The spectral sequences and parametric normal forms"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.3891","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":"sha256:16c87a363c675865fef0eef275bcadca33ebcd8a811fd05aef8a055a207c4c90","target":"record","created_at":"2026-05-18T03:21:32Z","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":"da091df5c2825250fc98c7b0c72a76423d5eb709b211955dec5a1c0bc150b3f1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2011-03-20T21:34:23Z","title_canon_sha256":"96f21e9fd1a61c5648515b0cc38df6b95400f5374949c3ecfd82ab15b855e3f4"},"schema_version":"1.0","source":{"id":"1103.3891","kind":"arxiv","version":1}},"canonical_sha256":"e3df7cdfdfbf09ffe3010ef9d3d97d7918216581598d54648183f7f47ace0a06","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e3df7cdfdfbf09ffe3010ef9d3d97d7918216581598d54648183f7f47ace0a06","first_computed_at":"2026-05-18T03:21:32.074513Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:21:32.074513Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"HZOgA2NqOZaIQUF6a21pDo4oO5qDHiCJsXeiiQqUlmn/4okwtom0my1qX/9SQ3rxriIh02v2XH9x+FdmakedBw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:21:32.074999Z","signed_message":"canonical_sha256_bytes"},"source_id":"1103.3891","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:16c87a363c675865fef0eef275bcadca33ebcd8a811fd05aef8a055a207c4c90","sha256:70d06480c4fe4da19442b835f454740d388e4021d15d3bddaca2932cd22c7977"],"state_sha256":"ae351f808e81a8f33c01686eaa23b16f0e7aa9e912aaac9abf0d42c9479c6618"}