{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:LDKCVQ7B32HFCD5JP5OAYXB4NX","short_pith_number":"pith:LDKCVQ7B","canonical_record":{"source":{"id":"1712.10203","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-29T12:28:47Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"04e0ffdb9776479046bf70f4a592467cd5b113db0bf67da3f2593189425efc0e","abstract_canon_sha256":"7ef082a88d9d74440f08af030eb566186130ea410725eabf2c8abdc759fc95c4"},"schema_version":"1.0"},"canonical_sha256":"58d42ac3e1de8e510fa97f5c0c5c3c6dffa4d3fce48d3cac1923bbb74aaa4c34","source":{"kind":"arxiv","id":"1712.10203","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.10203","created_at":"2026-05-17T23:58:14Z"},{"alias_kind":"arxiv_version","alias_value":"1712.10203v2","created_at":"2026-05-17T23:58:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.10203","created_at":"2026-05-17T23:58:14Z"},{"alias_kind":"pith_short_12","alias_value":"LDKCVQ7B32HF","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LDKCVQ7B32HFCD5J","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LDKCVQ7B","created_at":"2026-05-18T12:31:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:LDKCVQ7B32HFCD5JP5OAYXB4NX","target":"record","payload":{"canonical_record":{"source":{"id":"1712.10203","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-29T12:28:47Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"04e0ffdb9776479046bf70f4a592467cd5b113db0bf67da3f2593189425efc0e","abstract_canon_sha256":"7ef082a88d9d74440f08af030eb566186130ea410725eabf2c8abdc759fc95c4"},"schema_version":"1.0"},"canonical_sha256":"58d42ac3e1de8e510fa97f5c0c5c3c6dffa4d3fce48d3cac1923bbb74aaa4c34","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:58:14.712418Z","signature_b64":"KM1RjLL48QUzWjlTBZQVlRtv5U2jwTZQz5vz4AXom8I4osri1XVW0BO58C5/tqaN3NL6NrZFbeyZoryDEbi8Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"58d42ac3e1de8e510fa97f5c0c5c3c6dffa4d3fce48d3cac1923bbb74aaa4c34","last_reissued_at":"2026-05-17T23:58:14.711916Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:58:14.711916Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1712.10203","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":"2026-05-17T23:58:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZXDW7yidUdTxeKcc8JqpaECNQq7Jsba3cnborbE/XvpU4zqcQxVR4DtpfALD0YkPv38rlyHJCEcPI1flPo2gDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T07:16:25.943453Z"},"content_sha256":"f538527266bbd1f4f78149070175d07f8f2358bdfe168a382a7963d797c21bd8","schema_version":"1.0","event_id":"sha256:f538527266bbd1f4f78149070175d07f8f2358bdfe168a382a7963d797c21bd8"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:LDKCVQ7B32HFCD5JP5OAYXB4NX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Topological singular set of vector-valued maps, I: Applications to manifold-constrained Sobolev and BV spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.AP","authors_text":"Giacomo Canevari, Giandomenico Orlandi","submitted_at":"2017-12-29T12:28:47Z","abstract_excerpt":"We introduce an operator $\\mathbf{S}$ on vector-valued maps $u$ which has the ability to capture the relevant topological information carried by $u$. In particular, this operator is defined on maps that take values in a closed submanifold $N$ of the Euclidean space $\\mathbb{R}^m$, and coincides with the distributional Jacobian in case $N$ is a sphere. The range of $\\mathbf{S}$ is a set of maps whose values are flat chains with coefficients in a suitable normed abelian group. In this paper, we use $\\mathbf{S}$ to characterise strong limits of smooth, $N$-valued maps with respect to Sobolev norm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.10203","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":"2026-05-17T23:58:14Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/oP+egqq8G3fo6cdbPHAe7nF6igCd7TJosFXvpw0EGg2rJp6Pza3ccPe67llEO78ODU7vL493TyTHIW/s9CnBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-02T07:16:25.943790Z"},"content_sha256":"b3c9eee8cc0c5c3fcd25a2692fd1c4d3f80d6a5273e1ddbdea98daedcefb7f92","schema_version":"1.0","event_id":"sha256:b3c9eee8cc0c5c3fcd25a2692fd1c4d3f80d6a5273e1ddbdea98daedcefb7f92"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/LDKCVQ7B32HFCD5JP5OAYXB4NX/bundle.json","state_url":"https://pith.science/pith/LDKCVQ7B32HFCD5JP5OAYXB4NX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/LDKCVQ7B32HFCD5JP5OAYXB4NX/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":"2026-06-02T07:16:25Z","links":{"resolver":"https://pith.science/pith/LDKCVQ7B32HFCD5JP5OAYXB4NX","bundle":"https://pith.science/pith/LDKCVQ7B32HFCD5JP5OAYXB4NX/bundle.json","state":"https://pith.science/pith/LDKCVQ7B32HFCD5JP5OAYXB4NX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/LDKCVQ7B32HFCD5JP5OAYXB4NX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:LDKCVQ7B32HFCD5JP5OAYXB4NX","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":"7ef082a88d9d74440f08af030eb566186130ea410725eabf2c8abdc759fc95c4","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-29T12:28:47Z","title_canon_sha256":"04e0ffdb9776479046bf70f4a592467cd5b113db0bf67da3f2593189425efc0e"},"schema_version":"1.0","source":{"id":"1712.10203","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1712.10203","created_at":"2026-05-17T23:58:14Z"},{"alias_kind":"arxiv_version","alias_value":"1712.10203v2","created_at":"2026-05-17T23:58:14Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1712.10203","created_at":"2026-05-17T23:58:14Z"},{"alias_kind":"pith_short_12","alias_value":"LDKCVQ7B32HF","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_16","alias_value":"LDKCVQ7B32HFCD5J","created_at":"2026-05-18T12:31:28Z"},{"alias_kind":"pith_short_8","alias_value":"LDKCVQ7B","created_at":"2026-05-18T12:31:28Z"}],"graph_snapshots":[{"event_id":"sha256:b3c9eee8cc0c5c3fcd25a2692fd1c4d3f80d6a5273e1ddbdea98daedcefb7f92","target":"graph","created_at":"2026-05-17T23:58:14Z","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 introduce an operator $\\mathbf{S}$ on vector-valued maps $u$ which has the ability to capture the relevant topological information carried by $u$. In particular, this operator is defined on maps that take values in a closed submanifold $N$ of the Euclidean space $\\mathbb{R}^m$, and coincides with the distributional Jacobian in case $N$ is a sphere. The range of $\\mathbf{S}$ is a set of maps whose values are flat chains with coefficients in a suitable normed abelian group. In this paper, we use $\\mathbf{S}$ to characterise strong limits of smooth, $N$-valued maps with respect to Sobolev norm","authors_text":"Giacomo Canevari, Giandomenico Orlandi","cross_cats":["math.FA"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-29T12:28:47Z","title":"Topological singular set of vector-valued maps, I: Applications to manifold-constrained Sobolev and BV spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1712.10203","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:f538527266bbd1f4f78149070175d07f8f2358bdfe168a382a7963d797c21bd8","target":"record","created_at":"2026-05-17T23:58:14Z","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":"7ef082a88d9d74440f08af030eb566186130ea410725eabf2c8abdc759fc95c4","cross_cats_sorted":["math.FA"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-12-29T12:28:47Z","title_canon_sha256":"04e0ffdb9776479046bf70f4a592467cd5b113db0bf67da3f2593189425efc0e"},"schema_version":"1.0","source":{"id":"1712.10203","kind":"arxiv","version":2}},"canonical_sha256":"58d42ac3e1de8e510fa97f5c0c5c3c6dffa4d3fce48d3cac1923bbb74aaa4c34","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"58d42ac3e1de8e510fa97f5c0c5c3c6dffa4d3fce48d3cac1923bbb74aaa4c34","first_computed_at":"2026-05-17T23:58:14.711916Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:58:14.711916Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"KM1RjLL48QUzWjlTBZQVlRtv5U2jwTZQz5vz4AXom8I4osri1XVW0BO58C5/tqaN3NL6NrZFbeyZoryDEbi8Aw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:58:14.712418Z","signed_message":"canonical_sha256_bytes"},"source_id":"1712.10203","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f538527266bbd1f4f78149070175d07f8f2358bdfe168a382a7963d797c21bd8","sha256:b3c9eee8cc0c5c3fcd25a2692fd1c4d3f80d6a5273e1ddbdea98daedcefb7f92"],"state_sha256":"bc7727430c27f3b9ce901ff50486f6163a3110d5a902f4a14271ed70734a973a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"zrVtlI9ovhUl3dZVn/nrCBmAKP5S+wdwyb/5IUCmwSf7aWGFTsmckJoaroqn1JLAYtZoyQx3lS1biC531+62Aw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-02T07:16:25.945638Z","bundle_sha256":"6148ba1c8c6e4e12dea8ccb7be3bf97089f2f9ed35b8f00a1e7e19bed5f08a2d"}}