{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2019:2LXUOD4WXHKZWUQNQYY2B4CRXC","short_pith_number":"pith:2LXUOD4W","canonical_record":{"source":{"id":"1908.01990","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-08-06T07:19:13Z","cross_cats_sorted":["math.DG","math.MP","math.PR"],"title_canon_sha256":"3e5d4a209d05ed6426bb1d207d8b208160a8471e2cbf3b8ad26439b3b502e640","abstract_canon_sha256":"5807657c03c180097bd8654b33034ef07e17e3ce30aba9b5581a61caa42b886a"},"schema_version":"1.0"},"canonical_sha256":"d2ef470f96b9d59b520d8631a0f051b88b9a2b10543393fa84f43c24522934cf","source":{"kind":"arxiv","id":"1908.01990","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.01990","created_at":"2026-07-05T02:24:47Z"},{"alias_kind":"arxiv_version","alias_value":"1908.01990v3","created_at":"2026-07-05T02:24:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.01990","created_at":"2026-07-05T02:24:47Z"},{"alias_kind":"pith_short_12","alias_value":"2LXUOD4WXHKZ","created_at":"2026-07-05T02:24:47Z"},{"alias_kind":"pith_short_16","alias_value":"2LXUOD4WXHKZWUQN","created_at":"2026-07-05T02:24:47Z"},{"alias_kind":"pith_short_8","alias_value":"2LXUOD4W","created_at":"2026-07-05T02:24:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2019:2LXUOD4WXHKZWUQNQYY2B4CRXC","target":"record","payload":{"canonical_record":{"source":{"id":"1908.01990","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-08-06T07:19:13Z","cross_cats_sorted":["math.DG","math.MP","math.PR"],"title_canon_sha256":"3e5d4a209d05ed6426bb1d207d8b208160a8471e2cbf3b8ad26439b3b502e640","abstract_canon_sha256":"5807657c03c180097bd8654b33034ef07e17e3ce30aba9b5581a61caa42b886a"},"schema_version":"1.0"},"canonical_sha256":"d2ef470f96b9d59b520d8631a0f051b88b9a2b10543393fa84f43c24522934cf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T02:24:47.849241Z","signature_b64":"trPvyFsRIQYCSxpbv5PFZo563qpsENNhEOS4gydCh1+fnTJ5wnJHYK88qaXFhdxrJHqjPmiuGdf0OjLpktNYCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d2ef470f96b9d59b520d8631a0f051b88b9a2b10543393fa84f43c24522934cf","last_reissued_at":"2026-07-05T02:24:47.848850Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T02:24:47.848850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1908.01990","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-07-05T02:24:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"x/T/rVaZQvwqfqsKIjmQSLgRYvYL1lcZ6579QekZKDBZEeJzQuV983jygeb52PgX5xM8JDxax7OxRQuCWvwtDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T06:33:20.650127Z"},"content_sha256":"3d457543b43d3f68d9881ce4f60fefe6628c25e424f8865078453638ce11d322","schema_version":"1.0","event_id":"sha256:3d457543b43d3f68d9881ce4f60fefe6628c25e424f8865078453638ce11d322"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2019:2LXUOD4WXHKZWUQNQYY2B4CRXC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the Stochastic Processes on $7$-Dimensional Spheres","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.MP","math.PR"],"primary_cat":"math-ph","authors_text":"Adhitya Ronnie Effendie, Muhammad Farchani Rosyid, Nurfarisha","submitted_at":"2019-08-06T07:19:13Z","abstract_excerpt":"We studied isometric stochastic flows of a Stratonovich stochastic differential equation on spheres, i.e. on the standard sphere and Gromoll-Meyer exotic sphere. The standard sphere $S^7_s$ can be constructed as the quotient manifold $\\mathrm{Sp}(2, \\mathbb{H})/S^3$ with the so-called ${\\bullet}$-action of $S^3$, whereas the Gromoll-Meyer exotic sphere $\\Sigma^7_{GM}$ as the quotient manifold $\\mathrm{Sp}(2, \\mathbb{H})/S^3$ with respect to the so-called ${\\star}$-action of $S^3$. The Stratonovich stochastic differential equation which describes a continuous-time stochastic process on the stan"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.01990","kind":"arxiv","version":3},"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/1908.01990/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":"2026-07-05T02:24:47Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"PGeK0jGkLjOa1u4hj9keZJBXKA0BGB7upjejtJtme0CdfZSSvdU23fa9MwyvjVbO1Ib60VI+N3SCXbJhz4ZABQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-21T06:33:20.650459Z"},"content_sha256":"8a377c56ada3009a018fedd2af1ea29390c7986a3848c1e2fbef5200b3dd449d","schema_version":"1.0","event_id":"sha256:8a377c56ada3009a018fedd2af1ea29390c7986a3848c1e2fbef5200b3dd449d"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/2LXUOD4WXHKZWUQNQYY2B4CRXC/bundle.json","state_url":"https://pith.science/pith/2LXUOD4WXHKZWUQNQYY2B4CRXC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/2LXUOD4WXHKZWUQNQYY2B4CRXC/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":"2026-08-21T06:33:20Z","links":{"resolver":"https://pith.science/pith/2LXUOD4WXHKZWUQNQYY2B4CRXC","bundle":"https://pith.science/pith/2LXUOD4WXHKZWUQNQYY2B4CRXC/bundle.json","state":"https://pith.science/pith/2LXUOD4WXHKZWUQNQYY2B4CRXC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/2LXUOD4WXHKZWUQNQYY2B4CRXC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2019:2LXUOD4WXHKZWUQNQYY2B4CRXC","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":"5807657c03c180097bd8654b33034ef07e17e3ce30aba9b5581a61caa42b886a","cross_cats_sorted":["math.DG","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-08-06T07:19:13Z","title_canon_sha256":"3e5d4a209d05ed6426bb1d207d8b208160a8471e2cbf3b8ad26439b3b502e640"},"schema_version":"1.0","source":{"id":"1908.01990","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1908.01990","created_at":"2026-07-05T02:24:47Z"},{"alias_kind":"arxiv_version","alias_value":"1908.01990v3","created_at":"2026-07-05T02:24:47Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1908.01990","created_at":"2026-07-05T02:24:47Z"},{"alias_kind":"pith_short_12","alias_value":"2LXUOD4WXHKZ","created_at":"2026-07-05T02:24:47Z"},{"alias_kind":"pith_short_16","alias_value":"2LXUOD4WXHKZWUQN","created_at":"2026-07-05T02:24:47Z"},{"alias_kind":"pith_short_8","alias_value":"2LXUOD4W","created_at":"2026-07-05T02:24:47Z"}],"graph_snapshots":[{"event_id":"sha256:8a377c56ada3009a018fedd2af1ea29390c7986a3848c1e2fbef5200b3dd449d","target":"graph","created_at":"2026-07-05T02:24:47Z","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/1908.01990/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We studied isometric stochastic flows of a Stratonovich stochastic differential equation on spheres, i.e. on the standard sphere and Gromoll-Meyer exotic sphere. The standard sphere $S^7_s$ can be constructed as the quotient manifold $\\mathrm{Sp}(2, \\mathbb{H})/S^3$ with the so-called ${\\bullet}$-action of $S^3$, whereas the Gromoll-Meyer exotic sphere $\\Sigma^7_{GM}$ as the quotient manifold $\\mathrm{Sp}(2, \\mathbb{H})/S^3$ with respect to the so-called ${\\star}$-action of $S^3$. The Stratonovich stochastic differential equation which describes a continuous-time stochastic process on the stan","authors_text":"Adhitya Ronnie Effendie, Muhammad Farchani Rosyid, Nurfarisha","cross_cats":["math.DG","math.MP","math.PR"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-08-06T07:19:13Z","title":"On the Stochastic Processes on $7$-Dimensional Spheres"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1908.01990","kind":"arxiv","version":3},"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":"sha256:3d457543b43d3f68d9881ce4f60fefe6628c25e424f8865078453638ce11d322","target":"record","created_at":"2026-07-05T02:24:47Z","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":"5807657c03c180097bd8654b33034ef07e17e3ce30aba9b5581a61caa42b886a","cross_cats_sorted":["math.DG","math.MP","math.PR"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2019-08-06T07:19:13Z","title_canon_sha256":"3e5d4a209d05ed6426bb1d207d8b208160a8471e2cbf3b8ad26439b3b502e640"},"schema_version":"1.0","source":{"id":"1908.01990","kind":"arxiv","version":3}},"canonical_sha256":"d2ef470f96b9d59b520d8631a0f051b88b9a2b10543393fa84f43c24522934cf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d2ef470f96b9d59b520d8631a0f051b88b9a2b10543393fa84f43c24522934cf","first_computed_at":"2026-07-05T02:24:47.848850Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T02:24:47.848850Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"trPvyFsRIQYCSxpbv5PFZo563qpsENNhEOS4gydCh1+fnTJ5wnJHYK88qaXFhdxrJHqjPmiuGdf0OjLpktNYCw==","signature_status":"signed_v1","signed_at":"2026-07-05T02:24:47.849241Z","signed_message":"canonical_sha256_bytes"},"source_id":"1908.01990","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d457543b43d3f68d9881ce4f60fefe6628c25e424f8865078453638ce11d322","sha256:8a377c56ada3009a018fedd2af1ea29390c7986a3848c1e2fbef5200b3dd449d"],"state_sha256":"80246cf3b90505a0e0edac437dfe8cd008a687daef2ed9070a4c72512fc25631"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5t9IVDSaysrovQH3kYUbBVFQwXNiiPaBVYPSWZ0pwCYLj6oPCf6Z0gWXGeaF52KBN/dFkvoe3W9peAR6ER7YAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-21T06:33:20.654452Z","bundle_sha256":"2f66f2d44a51f6e19f82a4310a96ca8bbbcce1071b951b29b582d830a2643970"}}