{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2021:DYHZ2UGXKGTOLNNU2GORW5DWCN","short_pith_number":"pith:DYHZ2UGX","canonical_record":{"source":{"id":"2111.14528","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2021-11-29T13:40:31Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"483d027afd45190a3dfc063dfe850bc1f51a6681e8f06ed42f0fe333fd6bf264","abstract_canon_sha256":"1809aad94dadcdf7d1f0dc8428dfff6eb5ccf93fd81fa24263efbaef9f9e0a70"},"schema_version":"1.0"},"canonical_sha256":"1e0f9d50d751a6e5b5b4d19d1b747613530fe8fc2ae70854b3a99a51164f50c1","source":{"kind":"arxiv","id":"2111.14528","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.14528","created_at":"2026-07-05T11:11:28Z"},{"alias_kind":"arxiv_version","alias_value":"2111.14528v2","created_at":"2026-07-05T11:11:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.14528","created_at":"2026-07-05T11:11:28Z"},{"alias_kind":"pith_short_12","alias_value":"DYHZ2UGXKGTO","created_at":"2026-07-05T11:11:28Z"},{"alias_kind":"pith_short_16","alias_value":"DYHZ2UGXKGTOLNNU","created_at":"2026-07-05T11:11:28Z"},{"alias_kind":"pith_short_8","alias_value":"DYHZ2UGX","created_at":"2026-07-05T11:11:28Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2021:DYHZ2UGXKGTOLNNU2GORW5DWCN","target":"record","payload":{"canonical_record":{"source":{"id":"2111.14528","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2021-11-29T13:40:31Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"483d027afd45190a3dfc063dfe850bc1f51a6681e8f06ed42f0fe333fd6bf264","abstract_canon_sha256":"1809aad94dadcdf7d1f0dc8428dfff6eb5ccf93fd81fa24263efbaef9f9e0a70"},"schema_version":"1.0"},"canonical_sha256":"1e0f9d50d751a6e5b5b4d19d1b747613530fe8fc2ae70854b3a99a51164f50c1","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T11:11:28.874333Z","signature_b64":"7OsvN0c8ezQjIsoHrVNgKXXHiuH4FkijwP/QjnqVASXmPbsJu8TLKLGKphCWwGluPHQOsy9+Y5l7mdRlhsBNCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1e0f9d50d751a6e5b5b4d19d1b747613530fe8fc2ae70854b3a99a51164f50c1","last_reissued_at":"2026-07-05T11:11:28.873822Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T11:11:28.873822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2111.14528","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":"2026-07-05T11:11:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"UmaqYTnnwGPSMI7JEaUo0+NXFaTjccbEmsnsexNCqW5pnBXvRal3VIHhuxg2QAhEu2QvUNpP0iKTsS2lx3HrDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T09:59:25.403748Z"},"content_sha256":"b2007d9aa42d9c3f2df1a0c1072ad84723c287951289ee9a27d2d8ef8046d54f","schema_version":"1.0","event_id":"sha256:b2007d9aa42d9c3f2df1a0c1072ad84723c287951289ee9a27d2d8ef8046d54f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2021:DYHZ2UGXKGTOLNNU2GORW5DWCN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Reconstruction and interpolation of manifolds II: Inverse problems with partial data for distances observations and for the heat kernel","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.DG","authors_text":"Charles Fefferman, Hariharan Narayanan, Jinpeng Lu, Matti Lassas, Sergei Ivanov","submitted_at":"2021-11-29T13:40:31Z","abstract_excerpt":"We consider how a closed Riemannian manifold $M$ and its metric tensor $g$ can be approximately reconstructed from local distance measurements. Moreover, we consider an inverse problem of determining $(M,g)$ from limited knowledge on the heat kernel. In the part 1 of the paper, we considered the approximate construction of a smooth manifold in the case when one is given the noisy distances $\\tilde d(x,y)=d(x,y)+\\varepsilon_{x,y}$ for all points $x,y\\in X$, where $X$ is a $\\delta$-dense subset of $M$ and $|\\varepsilon_{x,y}|<\\delta$. In this part 2 of the paper, we consider a similar problem wi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.14528","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2111.14528/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":"2026-07-05T11:11:28Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LcWQriANaAc/hwKuD+tNBJ4jdnBYp31Vnc1pkGlHZMS7dj2i9aa2uqlvfDpUV+Dq7iSaaasbprzAX67LXOQzBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-09T09:59:25.404395Z"},"content_sha256":"60274936a8452be0600cf6cddc42c2048173b7febe1c0da206d7c88cf0637818","schema_version":"1.0","event_id":"sha256:60274936a8452be0600cf6cddc42c2048173b7febe1c0da206d7c88cf0637818"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DYHZ2UGXKGTOLNNU2GORW5DWCN/bundle.json","state_url":"https://pith.science/pith/DYHZ2UGXKGTOLNNU2GORW5DWCN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DYHZ2UGXKGTOLNNU2GORW5DWCN/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":"2026-08-09T09:59:25Z","links":{"resolver":"https://pith.science/pith/DYHZ2UGXKGTOLNNU2GORW5DWCN","bundle":"https://pith.science/pith/DYHZ2UGXKGTOLNNU2GORW5DWCN/bundle.json","state":"https://pith.science/pith/DYHZ2UGXKGTOLNNU2GORW5DWCN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DYHZ2UGXKGTOLNNU2GORW5DWCN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2021:DYHZ2UGXKGTOLNNU2GORW5DWCN","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":"1809aad94dadcdf7d1f0dc8428dfff6eb5ccf93fd81fa24263efbaef9f9e0a70","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2021-11-29T13:40:31Z","title_canon_sha256":"483d027afd45190a3dfc063dfe850bc1f51a6681e8f06ed42f0fe333fd6bf264"},"schema_version":"1.0","source":{"id":"2111.14528","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2111.14528","created_at":"2026-07-05T11:11:28Z"},{"alias_kind":"arxiv_version","alias_value":"2111.14528v2","created_at":"2026-07-05T11:11:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2111.14528","created_at":"2026-07-05T11:11:28Z"},{"alias_kind":"pith_short_12","alias_value":"DYHZ2UGXKGTO","created_at":"2026-07-05T11:11:28Z"},{"alias_kind":"pith_short_16","alias_value":"DYHZ2UGXKGTOLNNU","created_at":"2026-07-05T11:11:28Z"},{"alias_kind":"pith_short_8","alias_value":"DYHZ2UGX","created_at":"2026-07-05T11:11:28Z"}],"graph_snapshots":[{"event_id":"sha256:60274936a8452be0600cf6cddc42c2048173b7febe1c0da206d7c88cf0637818","target":"graph","created_at":"2026-07-05T11:11:28Z","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/2111.14528/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We consider how a closed Riemannian manifold $M$ and its metric tensor $g$ can be approximately reconstructed from local distance measurements. Moreover, we consider an inverse problem of determining $(M,g)$ from limited knowledge on the heat kernel. In the part 1 of the paper, we considered the approximate construction of a smooth manifold in the case when one is given the noisy distances $\\tilde d(x,y)=d(x,y)+\\varepsilon_{x,y}$ for all points $x,y\\in X$, where $X$ is a $\\delta$-dense subset of $M$ and $|\\varepsilon_{x,y}|<\\delta$. In this part 2 of the paper, we consider a similar problem wi","authors_text":"Charles Fefferman, Hariharan Narayanan, Jinpeng Lu, Matti Lassas, Sergei Ivanov","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2021-11-29T13:40:31Z","title":"Reconstruction and interpolation of manifolds II: Inverse problems with partial data for distances observations and for the heat kernel"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2111.14528","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:b2007d9aa42d9c3f2df1a0c1072ad84723c287951289ee9a27d2d8ef8046d54f","target":"record","created_at":"2026-07-05T11:11:28Z","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":"1809aad94dadcdf7d1f0dc8428dfff6eb5ccf93fd81fa24263efbaef9f9e0a70","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2021-11-29T13:40:31Z","title_canon_sha256":"483d027afd45190a3dfc063dfe850bc1f51a6681e8f06ed42f0fe333fd6bf264"},"schema_version":"1.0","source":{"id":"2111.14528","kind":"arxiv","version":2}},"canonical_sha256":"1e0f9d50d751a6e5b5b4d19d1b747613530fe8fc2ae70854b3a99a51164f50c1","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1e0f9d50d751a6e5b5b4d19d1b747613530fe8fc2ae70854b3a99a51164f50c1","first_computed_at":"2026-07-05T11:11:28.873822Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T11:11:28.873822Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"7OsvN0c8ezQjIsoHrVNgKXXHiuH4FkijwP/QjnqVASXmPbsJu8TLKLGKphCWwGluPHQOsy9+Y5l7mdRlhsBNCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T11:11:28.874333Z","signed_message":"canonical_sha256_bytes"},"source_id":"2111.14528","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b2007d9aa42d9c3f2df1a0c1072ad84723c287951289ee9a27d2d8ef8046d54f","sha256:60274936a8452be0600cf6cddc42c2048173b7febe1c0da206d7c88cf0637818"],"state_sha256":"d3acf66402146fea95813f1c6f83e774f841063902fd4d6ea77cca671d098d5a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"yVirZPZr8QiVCu4rGb6MVrWM/5tKc8sJx/fDLkw6my6U8srkdKyoEHjubB7/6PKyJgjkbxSJLjmeKTK96mYtCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-09T09:59:25.409446Z","bundle_sha256":"723f68be8da50e2dfb7063bc7e99bcec2a6416cd2b206b2d0cbc5b3e107b0188"}}