{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:Q3NPH46EGWHCEMPX4FPXZZIZ3N","short_pith_number":"pith:Q3NPH46E","canonical_record":{"source":{"id":"1811.09687","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-23T21:00:03Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"633e8e1ff098dd15fd5ef265134cf594095778854b219f4a522a485508bcb69e","abstract_canon_sha256":"0751615baece182cec2c7259f9eff3930ae2396a95feedc58e424b87b6e826f3"},"schema_version":"1.0"},"canonical_sha256":"86daf3f3c4358e2231f7e15f7ce519db568e28f560006e0c0b99a5fc3481e00f","source":{"kind":"arxiv","id":"1811.09687","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.09687","created_at":"2026-05-18T00:00:01Z"},{"alias_kind":"arxiv_version","alias_value":"1811.09687v1","created_at":"2026-05-18T00:00:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.09687","created_at":"2026-05-18T00:00:01Z"},{"alias_kind":"pith_short_12","alias_value":"Q3NPH46EGWHC","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"Q3NPH46EGWHCEMPX","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"Q3NPH46E","created_at":"2026-05-18T12:32:46Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:Q3NPH46EGWHCEMPX4FPXZZIZ3N","target":"record","payload":{"canonical_record":{"source":{"id":"1811.09687","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-23T21:00:03Z","cross_cats_sorted":["math.MG"],"title_canon_sha256":"633e8e1ff098dd15fd5ef265134cf594095778854b219f4a522a485508bcb69e","abstract_canon_sha256":"0751615baece182cec2c7259f9eff3930ae2396a95feedc58e424b87b6e826f3"},"schema_version":"1.0"},"canonical_sha256":"86daf3f3c4358e2231f7e15f7ce519db568e28f560006e0c0b99a5fc3481e00f","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:00:01.477143Z","signature_b64":"acbGJrcaPLyF8ERH3zG8F1D47vopgVWe3S7FFkFaKVVnaZj6EgUISj+jGfeURBrU0ipSNXXppDgKpT00M0t1Bw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86daf3f3c4358e2231f7e15f7ce519db568e28f560006e0c0b99a5fc3481e00f","last_reissued_at":"2026-05-18T00:00:01.476660Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:00:01.476660Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.09687","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":"2026-05-18T00:00:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"FatkIxRpVQ6i1p/drfwuxeshgAptjRfa+7zi/gMP+AAWpI2qUp2SeARgwxlS518p3B+jW97VDU7awbMWIy97Aw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T01:14:57.831998Z"},"content_sha256":"5aa344d27b03e4fb0ddbe0df7d9a28e5279c6ba79d0c4ccdf9c8a7aac2f94731","schema_version":"1.0","event_id":"sha256:5aa344d27b03e4fb0ddbe0df7d9a28e5279c6ba79d0c4ccdf9c8a7aac2f94731"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:Q3NPH46EGWHCEMPX4FPXZZIZ3N","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"An infinite-dimensional helix invariant under spherical projections","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MG"],"primary_cat":"math.PR","authors_text":"Zakhar Kabluchko","submitted_at":"2018-11-23T21:00:03Z","abstract_excerpt":"We classify all subsets $S$ of the projective Hilbert space with the following property: for every point $\\pm s_0\\in S$, the spherical projection of $S\\backslash\\{\\pm s_0\\}$ to the hyperplane orthogonal to $\\pm s_0$ is isometric to $S\\backslash\\{\\pm s_0\\}$. In probabilistic terms, this means that we characterize all zero-mean Gaussian processes $Z=(Z(t))_{t\\in T}$ with the property that for every $s_0\\in T$ the conditional distribution of $(Z(t))_{t\\in T}$ given that $Z(s_0)=0$ coincides with the distribution of $(\\varphi(t; s_0) Z(t))_{t\\in T}$ for some function $\\varphi(t;s_0)$. A basic exam"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.09687","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":"2026-05-18T00:00:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"cznnyshAHF6VBmzxDJWqAC4CoJEup57+96N/CWAhIjvoB19lGCEQc6WPBk0NmUEdXq7EO/FyaUXM4YHao5+KBw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-27T01:14:57.832649Z"},"content_sha256":"3296b565c06e4d9efc1c27d9c538795f52adf7e6cd64129cbd840d01fa53e9d0","schema_version":"1.0","event_id":"sha256:3296b565c06e4d9efc1c27d9c538795f52adf7e6cd64129cbd840d01fa53e9d0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q3NPH46EGWHCEMPX4FPXZZIZ3N/bundle.json","state_url":"https://pith.science/pith/Q3NPH46EGWHCEMPX4FPXZZIZ3N/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q3NPH46EGWHCEMPX4FPXZZIZ3N/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":"2026-05-27T01:14:57Z","links":{"resolver":"https://pith.science/pith/Q3NPH46EGWHCEMPX4FPXZZIZ3N","bundle":"https://pith.science/pith/Q3NPH46EGWHCEMPX4FPXZZIZ3N/bundle.json","state":"https://pith.science/pith/Q3NPH46EGWHCEMPX4FPXZZIZ3N/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q3NPH46EGWHCEMPX4FPXZZIZ3N/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:Q3NPH46EGWHCEMPX4FPXZZIZ3N","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":"0751615baece182cec2c7259f9eff3930ae2396a95feedc58e424b87b6e826f3","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-23T21:00:03Z","title_canon_sha256":"633e8e1ff098dd15fd5ef265134cf594095778854b219f4a522a485508bcb69e"},"schema_version":"1.0","source":{"id":"1811.09687","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.09687","created_at":"2026-05-18T00:00:01Z"},{"alias_kind":"arxiv_version","alias_value":"1811.09687v1","created_at":"2026-05-18T00:00:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.09687","created_at":"2026-05-18T00:00:01Z"},{"alias_kind":"pith_short_12","alias_value":"Q3NPH46EGWHC","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_16","alias_value":"Q3NPH46EGWHCEMPX","created_at":"2026-05-18T12:32:46Z"},{"alias_kind":"pith_short_8","alias_value":"Q3NPH46E","created_at":"2026-05-18T12:32:46Z"}],"graph_snapshots":[{"event_id":"sha256:3296b565c06e4d9efc1c27d9c538795f52adf7e6cd64129cbd840d01fa53e9d0","target":"graph","created_at":"2026-05-18T00:00:01Z","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 classify all subsets $S$ of the projective Hilbert space with the following property: for every point $\\pm s_0\\in S$, the spherical projection of $S\\backslash\\{\\pm s_0\\}$ to the hyperplane orthogonal to $\\pm s_0$ is isometric to $S\\backslash\\{\\pm s_0\\}$. In probabilistic terms, this means that we characterize all zero-mean Gaussian processes $Z=(Z(t))_{t\\in T}$ with the property that for every $s_0\\in T$ the conditional distribution of $(Z(t))_{t\\in T}$ given that $Z(s_0)=0$ coincides with the distribution of $(\\varphi(t; s_0) Z(t))_{t\\in T}$ for some function $\\varphi(t;s_0)$. A basic exam","authors_text":"Zakhar Kabluchko","cross_cats":["math.MG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-23T21:00:03Z","title":"An infinite-dimensional helix invariant under spherical projections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.09687","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":"sha256:5aa344d27b03e4fb0ddbe0df7d9a28e5279c6ba79d0c4ccdf9c8a7aac2f94731","target":"record","created_at":"2026-05-18T00:00:01Z","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":"0751615baece182cec2c7259f9eff3930ae2396a95feedc58e424b87b6e826f3","cross_cats_sorted":["math.MG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-23T21:00:03Z","title_canon_sha256":"633e8e1ff098dd15fd5ef265134cf594095778854b219f4a522a485508bcb69e"},"schema_version":"1.0","source":{"id":"1811.09687","kind":"arxiv","version":1}},"canonical_sha256":"86daf3f3c4358e2231f7e15f7ce519db568e28f560006e0c0b99a5fc3481e00f","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86daf3f3c4358e2231f7e15f7ce519db568e28f560006e0c0b99a5fc3481e00f","first_computed_at":"2026-05-18T00:00:01.476660Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:00:01.476660Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"acbGJrcaPLyF8ERH3zG8F1D47vopgVWe3S7FFkFaKVVnaZj6EgUISj+jGfeURBrU0ipSNXXppDgKpT00M0t1Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T00:00:01.477143Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.09687","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:5aa344d27b03e4fb0ddbe0df7d9a28e5279c6ba79d0c4ccdf9c8a7aac2f94731","sha256:3296b565c06e4d9efc1c27d9c538795f52adf7e6cd64129cbd840d01fa53e9d0"],"state_sha256":"75f0f9de45a8ed839a00d4cc97e8fb77a904acc62152bca16b12b378ef73743f"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"MLRr70TQ/T4IkpWUbrAIQBFGm3T8cWhjIuHwKYtp9yIupD+Lz43OcUN884FBUUI15DLA3iLypxBfqqRlK3nmCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-27T01:14:57.836169Z","bundle_sha256":"cecffb92288eb64d7fcf3229b21a645f9cba0ba8b4588ae7a90ba1b67b70d0e5"}}