{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:IHJQDAVYXMYDIEBVYV64WC3M6A","short_pith_number":"pith:IHJQDAVY","canonical_record":{"source":{"id":"1706.09596","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-06-29T07:06:11Z","cross_cats_sorted":[],"title_canon_sha256":"311f01fd2cd8c650cd6a210237f85a7504e983db0bcfaa7d19ab1fb108f28abf","abstract_canon_sha256":"69d097f9fb42c891cc4a2e0715b2c33565e7f467f3b58534d144aa31a05e5739"},"schema_version":"1.0"},"canonical_sha256":"41d30182b8bb30341035c57dcb0b6cf02bcdbf9748fa31d410c4c06c8ac4de92","source":{"kind":"arxiv","id":"1706.09596","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.09596","created_at":"2026-05-18T00:41:14Z"},{"alias_kind":"arxiv_version","alias_value":"1706.09596v1","created_at":"2026-05-18T00:41:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.09596","created_at":"2026-05-18T00:41:14Z"},{"alias_kind":"pith_short_12","alias_value":"IHJQDAVYXMYD","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IHJQDAVYXMYDIEBV","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IHJQDAVY","created_at":"2026-05-18T12:31:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:IHJQDAVYXMYDIEBVYV64WC3M6A","target":"record","payload":{"canonical_record":{"source":{"id":"1706.09596","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-06-29T07:06:11Z","cross_cats_sorted":[],"title_canon_sha256":"311f01fd2cd8c650cd6a210237f85a7504e983db0bcfaa7d19ab1fb108f28abf","abstract_canon_sha256":"69d097f9fb42c891cc4a2e0715b2c33565e7f467f3b58534d144aa31a05e5739"},"schema_version":"1.0"},"canonical_sha256":"41d30182b8bb30341035c57dcb0b6cf02bcdbf9748fa31d410c4c06c8ac4de92","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:41:14.476663Z","signature_b64":"1fAyrhYDA6aC0+eSWU8Lrr0IdiWGWCGMzvVO+/s+IjfygtIu+tNf2B0n4TiWJJM+QPD8eqX/9mBoQ3jvu4bQDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"41d30182b8bb30341035c57dcb0b6cf02bcdbf9748fa31d410c4c06c8ac4de92","last_reissued_at":"2026-05-18T00:41:14.476022Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:41:14.476022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1706.09596","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":"2026-05-18T00:41:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"976+84X5yafEFbjDgtkHyMdqgMkcpaKUzKre8l+UsYJOp8ZMhrhC1cG7bYGbLi6aE4vSr9BmNzSlSAJR1hyuAg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T09:57:24.984158Z"},"content_sha256":"eef70ef191192edda0043d7201339a62b13eefd84b5d0f1b57e7790dbeb73e0c","schema_version":"1.0","event_id":"sha256:eef70ef191192edda0043d7201339a62b13eefd84b5d0f1b57e7790dbeb73e0c"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:IHJQDAVYXMYDIEBVYV64WC3M6A","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Isometric immersions into manifolds with metallic structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Abhitosh Upadhyay, Julien Roth","submitted_at":"2017-06-29T07:06:11Z","abstract_excerpt":"We consider submanifolds into Riemannian manifold with metallic structures. We obtain some new results for hypersurfaces in these spaces and we express the fundamental theorem of submanifolds into products spaces in terms of metallic structures. Moreover, we define new structures called complex metallic structures. We show that these structures are linked with complex structures. Then, we consider submanifolds into Riemannian manifold with such structures with a focus on invariant submanifolds and hypersurfaces. We also express in particular the fundamental theorem of submanifolds of complex s"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.09596","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":"2026-05-18T00:41:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MWtp/rDRwwTWgmTTQrEKvn/eit1JcX7BSCiiyqgwen+c3YH7kH/G82FgGllukvr3nt2nD/n+UQpv4uxbbxWvBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T09:57:24.984526Z"},"content_sha256":"d9c2851b6e19b246e0b0f009183de648d2b3bc269843a6bf9e6561ef2f65455a","schema_version":"1.0","event_id":"sha256:d9c2851b6e19b246e0b0f009183de648d2b3bc269843a6bf9e6561ef2f65455a"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/IHJQDAVYXMYDIEBVYV64WC3M6A/bundle.json","state_url":"https://pith.science/pith/IHJQDAVYXMYDIEBVYV64WC3M6A/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/IHJQDAVYXMYDIEBVYV64WC3M6A/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":"2026-05-31T09:57:24Z","links":{"resolver":"https://pith.science/pith/IHJQDAVYXMYDIEBVYV64WC3M6A","bundle":"https://pith.science/pith/IHJQDAVYXMYDIEBVYV64WC3M6A/bundle.json","state":"https://pith.science/pith/IHJQDAVYXMYDIEBVYV64WC3M6A/state.json","well_known_bundle":"https://pith.science/.well-known/pith/IHJQDAVYXMYDIEBVYV64WC3M6A/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:IHJQDAVYXMYDIEBVYV64WC3M6A","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":"69d097f9fb42c891cc4a2e0715b2c33565e7f467f3b58534d144aa31a05e5739","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-06-29T07:06:11Z","title_canon_sha256":"311f01fd2cd8c650cd6a210237f85a7504e983db0bcfaa7d19ab1fb108f28abf"},"schema_version":"1.0","source":{"id":"1706.09596","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1706.09596","created_at":"2026-05-18T00:41:14Z"},{"alias_kind":"arxiv_version","alias_value":"1706.09596v1","created_at":"2026-05-18T00:41:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1706.09596","created_at":"2026-05-18T00:41:14Z"},{"alias_kind":"pith_short_12","alias_value":"IHJQDAVYXMYD","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_16","alias_value":"IHJQDAVYXMYDIEBV","created_at":"2026-05-18T12:31:21Z"},{"alias_kind":"pith_short_8","alias_value":"IHJQDAVY","created_at":"2026-05-18T12:31:21Z"}],"graph_snapshots":[{"event_id":"sha256:d9c2851b6e19b246e0b0f009183de648d2b3bc269843a6bf9e6561ef2f65455a","target":"graph","created_at":"2026-05-18T00:41:14Z","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 consider submanifolds into Riemannian manifold with metallic structures. We obtain some new results for hypersurfaces in these spaces and we express the fundamental theorem of submanifolds into products spaces in terms of metallic structures. Moreover, we define new structures called complex metallic structures. We show that these structures are linked with complex structures. Then, we consider submanifolds into Riemannian manifold with such structures with a focus on invariant submanifolds and hypersurfaces. We also express in particular the fundamental theorem of submanifolds of complex s","authors_text":"Abhitosh Upadhyay, Julien Roth","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-06-29T07:06:11Z","title":"Isometric immersions into manifolds with metallic structures"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.09596","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:eef70ef191192edda0043d7201339a62b13eefd84b5d0f1b57e7790dbeb73e0c","target":"record","created_at":"2026-05-18T00:41:14Z","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":"69d097f9fb42c891cc4a2e0715b2c33565e7f467f3b58534d144aa31a05e5739","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2017-06-29T07:06:11Z","title_canon_sha256":"311f01fd2cd8c650cd6a210237f85a7504e983db0bcfaa7d19ab1fb108f28abf"},"schema_version":"1.0","source":{"id":"1706.09596","kind":"arxiv","version":1}},"canonical_sha256":"41d30182b8bb30341035c57dcb0b6cf02bcdbf9748fa31d410c4c06c8ac4de92","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"41d30182b8bb30341035c57dcb0b6cf02bcdbf9748fa31d410c4c06c8ac4de92","first_computed_at":"2026-05-18T00:41:14.476022Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:41:14.476022Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1fAyrhYDA6aC0+eSWU8Lrr0IdiWGWCGMzvVO+/s+IjfygtIu+tNf2B0n4TiWJJM+QPD8eqX/9mBoQ3jvu4bQDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:41:14.476663Z","signed_message":"canonical_sha256_bytes"},"source_id":"1706.09596","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:eef70ef191192edda0043d7201339a62b13eefd84b5d0f1b57e7790dbeb73e0c","sha256:d9c2851b6e19b246e0b0f009183de648d2b3bc269843a6bf9e6561ef2f65455a"],"state_sha256":"5121e54030961996cf7f5a70ff2ad44590519e78fedf87299a0a09df273c7cd9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"hkDjftqoolP5LWKe80KbCkV/4Oj42eqrWnLJP1imxoJbsC+x27BMW6qptuZxYxCh6na8HceSWNo/uNkoloyQBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T09:57:24.986643Z","bundle_sha256":"4dbd5a974688053ade7d87af6f8ad94e3f6b23e04bf0b8ca6f77391931c4ba6f"}}