{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:2RRNN5FEZ2U336H2WATMIWEVF2","short_pith_number":"pith:2RRNN5FE","canonical_record":{"source":{"id":"1508.02979","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-08-12T16:26:43Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"bba114b2e8db4cf2bbcac4702b7b9766c8749a217c7fe8ff1c4d61f0f6a01086","abstract_canon_sha256":"7ee98f9d7774e96c0f81c326ddf8d8de22a0f31e2012ca04d2877915c26d74e2"},"schema_version":"1.0"},"canonical_sha256":"d462d6f4a4cea9bdf8fab026c458952ea36e4f707245b1bb872eb774144ccd3f","source":{"kind":"arxiv","id":"1508.02979","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.02979","created_at":"2026-05-18T01:35:23Z"},{"alias_kind":"arxiv_version","alias_value":"1508.02979v1","created_at":"2026-05-18T01:35:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.02979","created_at":"2026-05-18T01:35:23Z"},{"alias_kind":"pith_short_12","alias_value":"2RRNN5FEZ2U3","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2RRNN5FEZ2U336H2","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2RRNN5FE","created_at":"2026-05-18T12:29:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:2RRNN5FEZ2U336H2WATMIWEVF2","target":"record","payload":{"canonical_record":{"source":{"id":"1508.02979","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-08-12T16:26:43Z","cross_cats_sorted":["math.AG"],"title_canon_sha256":"bba114b2e8db4cf2bbcac4702b7b9766c8749a217c7fe8ff1c4d61f0f6a01086","abstract_canon_sha256":"7ee98f9d7774e96c0f81c326ddf8d8de22a0f31e2012ca04d2877915c26d74e2"},"schema_version":"1.0"},"canonical_sha256":"d462d6f4a4cea9bdf8fab026c458952ea36e4f707245b1bb872eb774144ccd3f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:35:23.232058Z","signature_b64":"VPUjz7z2GlMhPBMnnCcsXnmx6ku2sVRkm0P+Jnndlu09E7XyzELMsci97Hi3TxdzvPxK2weraqauhNBs4+YkAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d462d6f4a4cea9bdf8fab026c458952ea36e4f707245b1bb872eb774144ccd3f","last_reissued_at":"2026-05-18T01:35:23.231250Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:35:23.231250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1508.02979","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":"2026-05-18T01:35:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FuZvT8SVcgMD7dp4E57Jw6ADMAZaPvanKeck2Jt09sftUeM/CBqfomBNjPGXvXEamff549KtTsyao4L0gcEQCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T10:52:37.838795Z"},"content_sha256":"08863991b69d33ec60f8b1a5fc32d547b3779ec9324e170402ada2b47d476bea","schema_version":"1.0","event_id":"sha256:08863991b69d33ec60f8b1a5fc32d547b3779ec9324e170402ada2b47d476bea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:2RRNN5FEZ2U336H2WATMIWEVF2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Holomorphic families of $[\\lambda]-$primitive themes","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.CV","authors_text":"Daniel Barlet","submitted_at":"2015-08-12T16:26:43Z","abstract_excerpt":"This article is the continuation of  [B. 13-b]  where we show how the isomorphism class of a $[\\lambda]-$primitive theme with a given Bernstein polynomial may be characterized by a (small) finite number of complex parameters. We construct here a corresponding locally versal holomorphic deformation of $ [\\lambda]-$primitive themes for each given  Bernstein polynomial. Then we prove the universality of the corresponding \"canonical family\" in many cases. We also give some examples  where no local universal family exists."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02979","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":"2026-05-18T01:35:23Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"TNm+k3e2bW3fVjr//9Zx2Yt2xzFOM+BbMDosyGVnHXdLxhMnFue1h7j+mfqTm9QRIhqBv6PQCNATHsZKViGfBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T10:52:37.839136Z"},"content_sha256":"358d924eafc3a03926f9c1aed362db618db92ba75866d42b7b2adbcbc5b9b608","schema_version":"1.0","event_id":"sha256:358d924eafc3a03926f9c1aed362db618db92ba75866d42b7b2adbcbc5b9b608"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2RRNN5FEZ2U336H2WATMIWEVF2/bundle.json","state_url":"https://pith.science/pith/2RRNN5FEZ2U336H2WATMIWEVF2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2RRNN5FEZ2U336H2WATMIWEVF2/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":"2026-07-02T10:52:37Z","links":{"resolver":"https://pith.science/pith/2RRNN5FEZ2U336H2WATMIWEVF2","bundle":"https://pith.science/pith/2RRNN5FEZ2U336H2WATMIWEVF2/bundle.json","state":"https://pith.science/pith/2RRNN5FEZ2U336H2WATMIWEVF2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2RRNN5FEZ2U336H2WATMIWEVF2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:2RRNN5FEZ2U336H2WATMIWEVF2","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":"7ee98f9d7774e96c0f81c326ddf8d8de22a0f31e2012ca04d2877915c26d74e2","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-08-12T16:26:43Z","title_canon_sha256":"bba114b2e8db4cf2bbcac4702b7b9766c8749a217c7fe8ff1c4d61f0f6a01086"},"schema_version":"1.0","source":{"id":"1508.02979","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1508.02979","created_at":"2026-05-18T01:35:23Z"},{"alias_kind":"arxiv_version","alias_value":"1508.02979v1","created_at":"2026-05-18T01:35:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1508.02979","created_at":"2026-05-18T01:35:23Z"},{"alias_kind":"pith_short_12","alias_value":"2RRNN5FEZ2U3","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_16","alias_value":"2RRNN5FEZ2U336H2","created_at":"2026-05-18T12:29:02Z"},{"alias_kind":"pith_short_8","alias_value":"2RRNN5FE","created_at":"2026-05-18T12:29:02Z"}],"graph_snapshots":[{"event_id":"sha256:358d924eafc3a03926f9c1aed362db618db92ba75866d42b7b2adbcbc5b9b608","target":"graph","created_at":"2026-05-18T01:35:23Z","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":"This article is the continuation of  [B. 13-b]  where we show how the isomorphism class of a $[\\lambda]-$primitive theme with a given Bernstein polynomial may be characterized by a (small) finite number of complex parameters. We construct here a corresponding locally versal holomorphic deformation of $ [\\lambda]-$primitive themes for each given  Bernstein polynomial. Then we prove the universality of the corresponding \"canonical family\" in many cases. We also give some examples  where no local universal family exists.","authors_text":"Daniel Barlet","cross_cats":["math.AG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-08-12T16:26:43Z","title":"Holomorphic families of $[\\lambda]-$primitive themes"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02979","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":"sha256:08863991b69d33ec60f8b1a5fc32d547b3779ec9324e170402ada2b47d476bea","target":"record","created_at":"2026-05-18T01:35:23Z","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":"7ee98f9d7774e96c0f81c326ddf8d8de22a0f31e2012ca04d2877915c26d74e2","cross_cats_sorted":["math.AG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CV","submitted_at":"2015-08-12T16:26:43Z","title_canon_sha256":"bba114b2e8db4cf2bbcac4702b7b9766c8749a217c7fe8ff1c4d61f0f6a01086"},"schema_version":"1.0","source":{"id":"1508.02979","kind":"arxiv","version":1}},"canonical_sha256":"d462d6f4a4cea9bdf8fab026c458952ea36e4f707245b1bb872eb774144ccd3f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d462d6f4a4cea9bdf8fab026c458952ea36e4f707245b1bb872eb774144ccd3f","first_computed_at":"2026-05-18T01:35:23.231250Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:35:23.231250Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VPUjz7z2GlMhPBMnnCcsXnmx6ku2sVRkm0P+Jnndlu09E7XyzELMsci97Hi3TxdzvPxK2weraqauhNBs4+YkAg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:35:23.232058Z","signed_message":"canonical_sha256_bytes"},"source_id":"1508.02979","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:08863991b69d33ec60f8b1a5fc32d547b3779ec9324e170402ada2b47d476bea","sha256:358d924eafc3a03926f9c1aed362db618db92ba75866d42b7b2adbcbc5b9b608"],"state_sha256":"8aaba47c1030227442c955b1c483d40624daaa87ddb4341a39e1196695b3d7eb"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uYg3Xv8qrmXH1yh3takNk4vSwMM/pm0da6D8vrm+epa5hHUyNEJcNnZIlBBQZ/vM3yplrd2s84Uno9G1+A7rBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T10:52:37.841037Z","bundle_sha256":"fdcdcfe4f1827203357c67c34a2151c9c161ca2ddc5d5a233b8fabf9ab7bd5a4"}}