{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:P76IHDOZKQD5SY5IOJ2OP5QYOY","short_pith_number":"pith:P76IHDOZ","canonical_record":{"source":{"id":"1711.05359","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-11-15T00:03:24Z","cross_cats_sorted":[],"title_canon_sha256":"aab0e39d59b902c3c417addefc27bb2eadb19acc0a9fe18e4474ea8af33b3141","abstract_canon_sha256":"99e29a4e95cf2e8a9776887d7660d729c32b2141dd705f35cd49a2c1fde6b8d1"},"schema_version":"1.0"},"canonical_sha256":"7ffc838dd95407d963a87274e7f6187615c4d8140f13e1324dec798e7598420c","source":{"kind":"arxiv","id":"1711.05359","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.05359","created_at":"2026-05-18T00:30:33Z"},{"alias_kind":"arxiv_version","alias_value":"1711.05359v1","created_at":"2026-05-18T00:30:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.05359","created_at":"2026-05-18T00:30:33Z"},{"alias_kind":"pith_short_12","alias_value":"P76IHDOZKQD5","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"P76IHDOZKQD5SY5I","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"P76IHDOZ","created_at":"2026-05-18T12:31:37Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:P76IHDOZKQD5SY5IOJ2OP5QYOY","target":"record","payload":{"canonical_record":{"source":{"id":"1711.05359","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-11-15T00:03:24Z","cross_cats_sorted":[],"title_canon_sha256":"aab0e39d59b902c3c417addefc27bb2eadb19acc0a9fe18e4474ea8af33b3141","abstract_canon_sha256":"99e29a4e95cf2e8a9776887d7660d729c32b2141dd705f35cd49a2c1fde6b8d1"},"schema_version":"1.0"},"canonical_sha256":"7ffc838dd95407d963a87274e7f6187615c4d8140f13e1324dec798e7598420c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:33.558608Z","signature_b64":"baJ7yIwvgj3fwZF5Ck+BUKPhZ8csUZX17yVmggqZlQkQGyd5tSd0pv68p5A4BfpoKf7yRGRRzjhApKA7gH4FBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7ffc838dd95407d963a87274e7f6187615c4d8140f13e1324dec798e7598420c","last_reissued_at":"2026-05-18T00:30:33.557878Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:33.557878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1711.05359","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":"2026-05-18T00:30:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"wCWIal4gxuALJ8C6MSsQSvKhj7N1ncddyF37Srh8udZD1EuZYHtOnmgE17LmCfASkwEJj3Ci2ugf+r9l8+ZKDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T20:45:08.646637Z"},"content_sha256":"3d2947f8cffe19b5b5de3e3606179e8e5db2c5b4a9d02a20b1f5857f0cea2b5a","schema_version":"1.0","event_id":"sha256:3d2947f8cffe19b5b5de3e3606179e8e5db2c5b4a9d02a20b1f5857f0cea2b5a"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:P76IHDOZKQD5SY5IOJ2OP5QYOY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On Finite Gauss Transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Anatoly Eydelzon, Maxim Arnold","submitted_at":"2017-11-15T00:03:24Z","abstract_excerpt":"We present an invariant density for the finite Gauss transformation of the unit interval and discuss some properties of this transformation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.05359","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":"2026-05-18T00:30:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"5BRh56klMiWNKs9fNrXSNzhDmShxuI+R+LlD3r/kSX6fNGEK2OCnpNFSIlLk2HSs1hGoWpWSS5AOYHo2MbeyCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-07T20:45:08.647010Z"},"content_sha256":"b9b7709c757437f51c018c5098b9c0e542cc8ef7a29f694bfde7185e5b547ad0","schema_version":"1.0","event_id":"sha256:b9b7709c757437f51c018c5098b9c0e542cc8ef7a29f694bfde7185e5b547ad0"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/P76IHDOZKQD5SY5IOJ2OP5QYOY/bundle.json","state_url":"https://pith.science/pith/P76IHDOZKQD5SY5IOJ2OP5QYOY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/P76IHDOZKQD5SY5IOJ2OP5QYOY/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":"2026-06-07T20:45:08Z","links":{"resolver":"https://pith.science/pith/P76IHDOZKQD5SY5IOJ2OP5QYOY","bundle":"https://pith.science/pith/P76IHDOZKQD5SY5IOJ2OP5QYOY/bundle.json","state":"https://pith.science/pith/P76IHDOZKQD5SY5IOJ2OP5QYOY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/P76IHDOZKQD5SY5IOJ2OP5QYOY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:P76IHDOZKQD5SY5IOJ2OP5QYOY","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":"99e29a4e95cf2e8a9776887d7660d729c32b2141dd705f35cd49a2c1fde6b8d1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-11-15T00:03:24Z","title_canon_sha256":"aab0e39d59b902c3c417addefc27bb2eadb19acc0a9fe18e4474ea8af33b3141"},"schema_version":"1.0","source":{"id":"1711.05359","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1711.05359","created_at":"2026-05-18T00:30:33Z"},{"alias_kind":"arxiv_version","alias_value":"1711.05359v1","created_at":"2026-05-18T00:30:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1711.05359","created_at":"2026-05-18T00:30:33Z"},{"alias_kind":"pith_short_12","alias_value":"P76IHDOZKQD5","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_16","alias_value":"P76IHDOZKQD5SY5I","created_at":"2026-05-18T12:31:37Z"},{"alias_kind":"pith_short_8","alias_value":"P76IHDOZ","created_at":"2026-05-18T12:31:37Z"}],"graph_snapshots":[{"event_id":"sha256:b9b7709c757437f51c018c5098b9c0e542cc8ef7a29f694bfde7185e5b547ad0","target":"graph","created_at":"2026-05-18T00:30:33Z","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 present an invariant density for the finite Gauss transformation of the unit interval and discuss some properties of this transformation.","authors_text":"Anatoly Eydelzon, Maxim Arnold","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-11-15T00:03:24Z","title":"On Finite Gauss Transform"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.05359","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":"sha256:3d2947f8cffe19b5b5de3e3606179e8e5db2c5b4a9d02a20b1f5857f0cea2b5a","target":"record","created_at":"2026-05-18T00:30:33Z","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":"99e29a4e95cf2e8a9776887d7660d729c32b2141dd705f35cd49a2c1fde6b8d1","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2017-11-15T00:03:24Z","title_canon_sha256":"aab0e39d59b902c3c417addefc27bb2eadb19acc0a9fe18e4474ea8af33b3141"},"schema_version":"1.0","source":{"id":"1711.05359","kind":"arxiv","version":1}},"canonical_sha256":"7ffc838dd95407d963a87274e7f6187615c4d8140f13e1324dec798e7598420c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7ffc838dd95407d963a87274e7f6187615c4d8140f13e1324dec798e7598420c","first_computed_at":"2026-05-18T00:30:33.557878Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:33.557878Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"baJ7yIwvgj3fwZF5Ck+BUKPhZ8csUZX17yVmggqZlQkQGyd5tSd0pv68p5A4BfpoKf7yRGRRzjhApKA7gH4FBQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:33.558608Z","signed_message":"canonical_sha256_bytes"},"source_id":"1711.05359","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d2947f8cffe19b5b5de3e3606179e8e5db2c5b4a9d02a20b1f5857f0cea2b5a","sha256:b9b7709c757437f51c018c5098b9c0e542cc8ef7a29f694bfde7185e5b547ad0"],"state_sha256":"6060ee04c3567142f3294b47e9c383afbe2ebe8249b00d8ccef95fbe114801db"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Xzh1z4MhNm8OivcCWCnMj58Ue3O4Jn2wyA2iFcbMUoFxtUzvE7y2K8pTyuFFBgIJ3VMY3kTcYXmtBXuom6MOBg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-07T20:45:08.650355Z","bundle_sha256":"f97323a80ea564a1dcdf388d937b7c5a0e9a579369d417e3856a301fc2cb5eed"}}