{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2006:XC6VJW7KYBJNQ5IWOJ7DMLDVRI","short_pith_number":"pith:XC6VJW7K","canonical_record":{"source":{"id":"math/0612449","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CV","submitted_at":"2006-12-15T15:14:08Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"da6dfddba08dd009e616486fa69194909f83295d94bbd06a7b2d2925c34742c7","abstract_canon_sha256":"14359808b7d6119f889dce7cdf9eb9d43ab2d93cd17165f27cd74c32b8aed1af"},"schema_version":"1.0"},"canonical_sha256":"b8bd54dbeac052d87516727e362c758a2c92e527067261ae1ae09f55370a7835","source":{"kind":"arxiv","id":"math/0612449","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0612449","created_at":"2026-07-04T14:58:03Z"},{"alias_kind":"arxiv_version","alias_value":"math/0612449v1","created_at":"2026-07-04T14:58:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0612449","created_at":"2026-07-04T14:58:03Z"},{"alias_kind":"pith_short_12","alias_value":"XC6VJW7KYBJN","created_at":"2026-07-04T14:58:03Z"},{"alias_kind":"pith_short_16","alias_value":"XC6VJW7KYBJNQ5IW","created_at":"2026-07-04T14:58:03Z"},{"alias_kind":"pith_short_8","alias_value":"XC6VJW7K","created_at":"2026-07-04T14:58:03Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2006:XC6VJW7KYBJNQ5IWOJ7DMLDVRI","target":"record","payload":{"canonical_record":{"source":{"id":"math/0612449","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.CV","submitted_at":"2006-12-15T15:14:08Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"da6dfddba08dd009e616486fa69194909f83295d94bbd06a7b2d2925c34742c7","abstract_canon_sha256":"14359808b7d6119f889dce7cdf9eb9d43ab2d93cd17165f27cd74c32b8aed1af"},"schema_version":"1.0"},"canonical_sha256":"b8bd54dbeac052d87516727e362c758a2c92e527067261ae1ae09f55370a7835","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-04T14:58:03.656670Z","signature_b64":"y4tdiBJAccVh0M2BmGUXBE1A0QpxN3wVzKjHC+ZK+64ly4OgLTCPNvKq4jdh0sGgU6JDFFIuG0BF2ybOhSR7Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b8bd54dbeac052d87516727e362c758a2c92e527067261ae1ae09f55370a7835","last_reissued_at":"2026-07-04T14:58:03.656240Z","signature_status":"signed_v1","first_computed_at":"2026-07-04T14:58:03.656240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0612449","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":"2026-07-04T14:58:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WqYWPYEBiNjHSyiJ4SkB5DfxNw1ckJy7XCNZS+Yy//IhNJY5LBy6CnIOYMVPh46aFHf0TW08xSonW11fBRlQBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T20:48:28.455818Z"},"content_sha256":"c691f11ff9598fd6e95dd6fa5749bd70fc08cdbda9543cf3c0676418c61ae0b4","schema_version":"1.0","event_id":"sha256:c691f11ff9598fd6e95dd6fa5749bd70fc08cdbda9543cf3c0676418c61ae0b4"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2006:XC6VJW7KYBJNQ5IWOJ7DMLDVRI","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Embeddings of submanifolds and normal bundles","license":"","headline":"","cross_cats":["math.DG"],"primary_cat":"math.CV","authors_text":"Filippo Bracci, Francesca Tovena, Marco Abate","submitted_at":"2006-12-15T15:14:08Z","abstract_excerpt":"This paper is devoted to the study of the embeddings of a complex submanifold $S$ inside a larger complex manifold $M$; in particular, we are interested in comparing the embedding of $S$ in $M$ with the embedding of $S$ as the zero section in the total space of the normal bundle $N_S$ of $S$ in $M$. We explicitely describe some cohomological classes allowing to measure the difference between the two embeddings, in the spirit of the work by Grauert, Griffiths, and Camacho-Movasati-Sad; we are also able to explain the geometrical meaning of the separate vanishing of these classes. Our results ho"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0612449","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/math/0612449/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-04T14:58:03Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CloGDIW1UaQJRhiLtK8jLb0l2fuNAFfMT5biL3jR9v77NHW+idtE/aiFW+hMZWfFy5gU6aEumVR4CDB3YGRtCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-10T20:48:28.456753Z"},"content_sha256":"9932018f6e71a2bd6b549db6ca63d3620edd5bb3204790a2c9e29f1a5085d4fc","schema_version":"1.0","event_id":"sha256:9932018f6e71a2bd6b549db6ca63d3620edd5bb3204790a2c9e29f1a5085d4fc"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/XC6VJW7KYBJNQ5IWOJ7DMLDVRI/bundle.json","state_url":"https://pith.science/pith/XC6VJW7KYBJNQ5IWOJ7DMLDVRI/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/XC6VJW7KYBJNQ5IWOJ7DMLDVRI/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":"2026-08-10T20:48:28Z","links":{"resolver":"https://pith.science/pith/XC6VJW7KYBJNQ5IWOJ7DMLDVRI","bundle":"https://pith.science/pith/XC6VJW7KYBJNQ5IWOJ7DMLDVRI/bundle.json","state":"https://pith.science/pith/XC6VJW7KYBJNQ5IWOJ7DMLDVRI/state.json","well_known_bundle":"https://pith.science/.well-known/pith/XC6VJW7KYBJNQ5IWOJ7DMLDVRI/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:XC6VJW7KYBJNQ5IWOJ7DMLDVRI","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":"14359808b7d6119f889dce7cdf9eb9d43ab2d93cd17165f27cd74c32b8aed1af","cross_cats_sorted":["math.DG"],"license":"","primary_cat":"math.CV","submitted_at":"2006-12-15T15:14:08Z","title_canon_sha256":"da6dfddba08dd009e616486fa69194909f83295d94bbd06a7b2d2925c34742c7"},"schema_version":"1.0","source":{"id":"math/0612449","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0612449","created_at":"2026-07-04T14:58:03Z"},{"alias_kind":"arxiv_version","alias_value":"math/0612449v1","created_at":"2026-07-04T14:58:03Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0612449","created_at":"2026-07-04T14:58:03Z"},{"alias_kind":"pith_short_12","alias_value":"XC6VJW7KYBJN","created_at":"2026-07-04T14:58:03Z"},{"alias_kind":"pith_short_16","alias_value":"XC6VJW7KYBJNQ5IW","created_at":"2026-07-04T14:58:03Z"},{"alias_kind":"pith_short_8","alias_value":"XC6VJW7K","created_at":"2026-07-04T14:58:03Z"}],"graph_snapshots":[{"event_id":"sha256:9932018f6e71a2bd6b549db6ca63d3620edd5bb3204790a2c9e29f1a5085d4fc","target":"graph","created_at":"2026-07-04T14:58:03Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/math/0612449/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper is devoted to the study of the embeddings of a complex submanifold $S$ inside a larger complex manifold $M$; in particular, we are interested in comparing the embedding of $S$ in $M$ with the embedding of $S$ as the zero section in the total space of the normal bundle $N_S$ of $S$ in $M$. We explicitely describe some cohomological classes allowing to measure the difference between the two embeddings, in the spirit of the work by Grauert, Griffiths, and Camacho-Movasati-Sad; we are also able to explain the geometrical meaning of the separate vanishing of these classes. Our results ho","authors_text":"Filippo Bracci, Francesca Tovena, Marco Abate","cross_cats":["math.DG"],"headline":"","license":"","primary_cat":"math.CV","submitted_at":"2006-12-15T15:14:08Z","title":"Embeddings of submanifolds and normal bundles"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0612449","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:c691f11ff9598fd6e95dd6fa5749bd70fc08cdbda9543cf3c0676418c61ae0b4","target":"record","created_at":"2026-07-04T14:58:03Z","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":"14359808b7d6119f889dce7cdf9eb9d43ab2d93cd17165f27cd74c32b8aed1af","cross_cats_sorted":["math.DG"],"license":"","primary_cat":"math.CV","submitted_at":"2006-12-15T15:14:08Z","title_canon_sha256":"da6dfddba08dd009e616486fa69194909f83295d94bbd06a7b2d2925c34742c7"},"schema_version":"1.0","source":{"id":"math/0612449","kind":"arxiv","version":1}},"canonical_sha256":"b8bd54dbeac052d87516727e362c758a2c92e527067261ae1ae09f55370a7835","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b8bd54dbeac052d87516727e362c758a2c92e527067261ae1ae09f55370a7835","first_computed_at":"2026-07-04T14:58:03.656240Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-04T14:58:03.656240Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y4tdiBJAccVh0M2BmGUXBE1A0QpxN3wVzKjHC+ZK+64ly4OgLTCPNvKq4jdh0sGgU6JDFFIuG0BF2ybOhSR7Aw==","signature_status":"signed_v1","signed_at":"2026-07-04T14:58:03.656670Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0612449","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:c691f11ff9598fd6e95dd6fa5749bd70fc08cdbda9543cf3c0676418c61ae0b4","sha256:9932018f6e71a2bd6b549db6ca63d3620edd5bb3204790a2c9e29f1a5085d4fc"],"state_sha256":"042a2737dd66271fe62917e0e6a73a6df079c71de165e162eafe35a05a013fe2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x+u2Kpl9seSTfNdlY574H3wcmiAH8wY61YvOgAst3HFQb4PaawVfUQG99iTUdzSR+7+3ljEET92X+iNJYGZMAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-10T20:48:28.492928Z","bundle_sha256":"8ccf7f9a9479b6a6fef8921f3ef81420a51190b41ab45c682eb5ad294e74aab7"}}