{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:O7LYDNEIZKOAHLEXENP4FCA7R2","short_pith_number":"pith:O7LYDNEI","canonical_record":{"source":{"id":"1806.05257","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-06-13T20:28:32Z","cross_cats_sorted":[],"title_canon_sha256":"da16c79f7f2c8275311ab2dbc11a5726a554caaf9c21047af09049c007616e16","abstract_canon_sha256":"0831aca26795335779cb3a3f3d290d96c0fe42d679fa1707c27ae08910b26b06"},"schema_version":"1.0"},"canonical_sha256":"77d781b488ca9c03ac97235fc2881f8e93e8e46b3b6addcdecf3a23d0c646852","source":{"kind":"arxiv","id":"1806.05257","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.05257","created_at":"2026-05-17T23:51:05Z"},{"alias_kind":"arxiv_version","alias_value":"1806.05257v2","created_at":"2026-05-17T23:51:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.05257","created_at":"2026-05-17T23:51:05Z"},{"alias_kind":"pith_short_12","alias_value":"O7LYDNEIZKOA","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"O7LYDNEIZKOAHLEX","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"O7LYDNEI","created_at":"2026-05-18T12:32:43Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:O7LYDNEIZKOAHLEXENP4FCA7R2","target":"record","payload":{"canonical_record":{"source":{"id":"1806.05257","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-06-13T20:28:32Z","cross_cats_sorted":[],"title_canon_sha256":"da16c79f7f2c8275311ab2dbc11a5726a554caaf9c21047af09049c007616e16","abstract_canon_sha256":"0831aca26795335779cb3a3f3d290d96c0fe42d679fa1707c27ae08910b26b06"},"schema_version":"1.0"},"canonical_sha256":"77d781b488ca9c03ac97235fc2881f8e93e8e46b3b6addcdecf3a23d0c646852","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:05.746168Z","signature_b64":"t2EPVKY8GbHrr35wgcQ6wGh6Pk3t5WVVvYJPbDLdkt26eE0/xnLLOw0Kuf125v7yVaykeGzvFVZjPGBhWZ0vAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"77d781b488ca9c03ac97235fc2881f8e93e8e46b3b6addcdecf3a23d0c646852","last_reissued_at":"2026-05-17T23:51:05.745657Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:05.745657Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1806.05257","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":"2026-05-17T23:51:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"fLBeZroD1FezMsSgZBPXkB+JkZKoNPQyS3LBay+dsywCLoRXy2WHcOeqlBbjxlxQNhQARQsPS2N8bQMFgSgLAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T18:30:18.808811Z"},"content_sha256":"35c366a1a29bd698f4af168f64b775d18cb8aba23c496882305e8aaa91b3809d","schema_version":"1.0","event_id":"sha256:35c366a1a29bd698f4af168f64b775d18cb8aba23c496882305e8aaa91b3809d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:O7LYDNEIZKOAHLEXENP4FCA7R2","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Distance difference representations of Riemannian manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Sergei Ivanov","submitted_at":"2018-06-13T20:28:32Z","abstract_excerpt":"Let $M$ be a complete Riemannian manifold and $F\\subset M$ a set with a nonempty interior. For every $x\\in M$, let $D_x$ denote the function on $F\\times F$ defined by $D_x(y,z)=d(x,y)-d(x,z)$ where $d$ is the geodesic distance in $M$. The map $x\\mapsto D_x$ from $M$ to the space of continuous functions on $F\\times F$, denoted by $\\mathcal D_F$, is called a distance difference representation of $M$. This representation, introduced recently by M. Lassas and T. Saksala, is motivated by geophysical imaging among other things.\n  We prove that the distance difference representation $\\mathcal D_F$ is"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05257","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":"2026-05-17T23:51:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MAdxvM+sIWShtRqflXc62C9cSWaoKs9W6IBYmq1BaOahL6PlcasSIG+5UPxiF3ECvJwpOKotym4E4KsKG3gNDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-23T18:30:18.809151Z"},"content_sha256":"419e29bdd3732767f5a44d8acdebb65907e0497b982420f97579ddaf33d0c71f","schema_version":"1.0","event_id":"sha256:419e29bdd3732767f5a44d8acdebb65907e0497b982420f97579ddaf33d0c71f"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/O7LYDNEIZKOAHLEXENP4FCA7R2/bundle.json","state_url":"https://pith.science/pith/O7LYDNEIZKOAHLEXENP4FCA7R2/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/O7LYDNEIZKOAHLEXENP4FCA7R2/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":"2026-06-23T18:30:18Z","links":{"resolver":"https://pith.science/pith/O7LYDNEIZKOAHLEXENP4FCA7R2","bundle":"https://pith.science/pith/O7LYDNEIZKOAHLEXENP4FCA7R2/bundle.json","state":"https://pith.science/pith/O7LYDNEIZKOAHLEXENP4FCA7R2/state.json","well_known_bundle":"https://pith.science/.well-known/pith/O7LYDNEIZKOAHLEXENP4FCA7R2/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:O7LYDNEIZKOAHLEXENP4FCA7R2","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":"0831aca26795335779cb3a3f3d290d96c0fe42d679fa1707c27ae08910b26b06","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-06-13T20:28:32Z","title_canon_sha256":"da16c79f7f2c8275311ab2dbc11a5726a554caaf9c21047af09049c007616e16"},"schema_version":"1.0","source":{"id":"1806.05257","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.05257","created_at":"2026-05-17T23:51:05Z"},{"alias_kind":"arxiv_version","alias_value":"1806.05257v2","created_at":"2026-05-17T23:51:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.05257","created_at":"2026-05-17T23:51:05Z"},{"alias_kind":"pith_short_12","alias_value":"O7LYDNEIZKOA","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_16","alias_value":"O7LYDNEIZKOAHLEX","created_at":"2026-05-18T12:32:43Z"},{"alias_kind":"pith_short_8","alias_value":"O7LYDNEI","created_at":"2026-05-18T12:32:43Z"}],"graph_snapshots":[{"event_id":"sha256:419e29bdd3732767f5a44d8acdebb65907e0497b982420f97579ddaf33d0c71f","target":"graph","created_at":"2026-05-17T23:51:05Z","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":"Let $M$ be a complete Riemannian manifold and $F\\subset M$ a set with a nonempty interior. For every $x\\in M$, let $D_x$ denote the function on $F\\times F$ defined by $D_x(y,z)=d(x,y)-d(x,z)$ where $d$ is the geodesic distance in $M$. The map $x\\mapsto D_x$ from $M$ to the space of continuous functions on $F\\times F$, denoted by $\\mathcal D_F$, is called a distance difference representation of $M$. This representation, introduced recently by M. Lassas and T. Saksala, is motivated by geophysical imaging among other things.\n  We prove that the distance difference representation $\\mathcal D_F$ is","authors_text":"Sergei Ivanov","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-06-13T20:28:32Z","title":"Distance difference representations of Riemannian manifolds"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.05257","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":"sha256:35c366a1a29bd698f4af168f64b775d18cb8aba23c496882305e8aaa91b3809d","target":"record","created_at":"2026-05-17T23:51:05Z","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":"0831aca26795335779cb3a3f3d290d96c0fe42d679fa1707c27ae08910b26b06","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2018-06-13T20:28:32Z","title_canon_sha256":"da16c79f7f2c8275311ab2dbc11a5726a554caaf9c21047af09049c007616e16"},"schema_version":"1.0","source":{"id":"1806.05257","kind":"arxiv","version":2}},"canonical_sha256":"77d781b488ca9c03ac97235fc2881f8e93e8e46b3b6addcdecf3a23d0c646852","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"77d781b488ca9c03ac97235fc2881f8e93e8e46b3b6addcdecf3a23d0c646852","first_computed_at":"2026-05-17T23:51:05.745657Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:05.745657Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"t2EPVKY8GbHrr35wgcQ6wGh6Pk3t5WVVvYJPbDLdkt26eE0/xnLLOw0Kuf125v7yVaykeGzvFVZjPGBhWZ0vAw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:05.746168Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.05257","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:35c366a1a29bd698f4af168f64b775d18cb8aba23c496882305e8aaa91b3809d","sha256:419e29bdd3732767f5a44d8acdebb65907e0497b982420f97579ddaf33d0c71f"],"state_sha256":"3cde1eaeec4ccee47336e87758dd398dfa4e5757eb2168e46cec98c2dddc41d2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"6h+oFJegeeyYEoAXtLrBybfxFna3ukis2LHhlll3qOi1sGJ8qqNXmwXytobPa/A/UNLIBmDi7tTweQWKINtLBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-23T18:30:18.811005Z","bundle_sha256":"c29e15b2355d99dfa418b3b0fab86e87e4d7f008448272fe07014331aec79561"}}