{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:DMJ2VQBTZTAYQV4ZNDZXQPHAUH","short_pith_number":"pith:DMJ2VQBT","canonical_record":{"source":{"id":"1811.03490","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-08T15:25:57Z","cross_cats_sorted":[],"title_canon_sha256":"d2590a8b4196f7659be0553226bb62483c0ba030293668236e40b94a13beb059","abstract_canon_sha256":"d70f72dc2948a3af62afef120c9aea157ca40012d8ef3597f50ff97efdc84da0"},"schema_version":"1.0"},"canonical_sha256":"1b13aac033ccc188579968f3783ce0a1c9223223fc62b419c15d37ced0292ed7","source":{"kind":"arxiv","id":"1811.03490","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.03490","created_at":"2026-05-18T00:01:15Z"},{"alias_kind":"arxiv_version","alias_value":"1811.03490v1","created_at":"2026-05-18T00:01:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.03490","created_at":"2026-05-18T00:01:15Z"},{"alias_kind":"pith_short_12","alias_value":"DMJ2VQBTZTAY","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DMJ2VQBTZTAYQV4Z","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DMJ2VQBT","created_at":"2026-05-18T12:32:19Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:DMJ2VQBTZTAYQV4ZNDZXQPHAUH","target":"record","payload":{"canonical_record":{"source":{"id":"1811.03490","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-08T15:25:57Z","cross_cats_sorted":[],"title_canon_sha256":"d2590a8b4196f7659be0553226bb62483c0ba030293668236e40b94a13beb059","abstract_canon_sha256":"d70f72dc2948a3af62afef120c9aea157ca40012d8ef3597f50ff97efdc84da0"},"schema_version":"1.0"},"canonical_sha256":"1b13aac033ccc188579968f3783ce0a1c9223223fc62b419c15d37ced0292ed7","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:01:15.985498Z","signature_b64":"UjQUL1dinQ7JzowGtXt6xSw6QCXJ1bX687k1QyF8emJ/yFvyWbc0oWSqNSwMkv1NFv9PWvpYGrahEpvs4eJZDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"1b13aac033ccc188579968f3783ce0a1c9223223fc62b419c15d37ced0292ed7","last_reissued_at":"2026-05-18T00:01:15.984904Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:01:15.984904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1811.03490","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":"2026-05-18T00:01:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"e4bBpcCv2+SVa3J+kyfa6/MK9Hdi+S3zOzo/6W11WFjUwxMxc9fG73BOa2c4vxfZSHV/Rpqc5A4ExOgz2gBHDQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:07:27.926086Z"},"content_sha256":"f5edb9c6d1c5d2d0ed5bcc0627b53a0809ee90637eb07c660e75536113efa2d3","schema_version":"1.0","event_id":"sha256:f5edb9c6d1c5d2d0ed5bcc0627b53a0809ee90637eb07c660e75536113efa2d3"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:DMJ2VQBTZTAYQV4ZNDZXQPHAUH","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A Noether theorem for random locations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jie Shen, Shunlong Luo, Yi Shen","submitted_at":"2018-11-08T15:25:57Z","abstract_excerpt":"We propose a unified framework for random locations exhibiting some probabilistic symmetries such as stationarity, self-similarity, etc. A theorem of Noether's type is proved, which gives rise to a conservation law describing the change of the density function of a random location as the interval of interest changes. We also discuss the boundary and near boundary behavior of the distributions of the random locations."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.03490","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":"2026-05-18T00:01:15Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vaUcAJvz2oGJ6AoReQ0WDt4aYp3gmo3fJjh47LmmQsLk8IY1/zHGNsQ2tnAWI9XrBxquiZz8Hh37YL2VTvsxBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-31T23:07:27.926798Z"},"content_sha256":"82ddeef0c71acc8f28dbfb8ec58646d3ebda0f8b7de9c288defb722e5e44c0a9","schema_version":"1.0","event_id":"sha256:82ddeef0c71acc8f28dbfb8ec58646d3ebda0f8b7de9c288defb722e5e44c0a9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/DMJ2VQBTZTAYQV4ZNDZXQPHAUH/bundle.json","state_url":"https://pith.science/pith/DMJ2VQBTZTAYQV4ZNDZXQPHAUH/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/DMJ2VQBTZTAYQV4ZNDZXQPHAUH/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":"2026-05-31T23:07:27Z","links":{"resolver":"https://pith.science/pith/DMJ2VQBTZTAYQV4ZNDZXQPHAUH","bundle":"https://pith.science/pith/DMJ2VQBTZTAYQV4ZNDZXQPHAUH/bundle.json","state":"https://pith.science/pith/DMJ2VQBTZTAYQV4ZNDZXQPHAUH/state.json","well_known_bundle":"https://pith.science/.well-known/pith/DMJ2VQBTZTAYQV4ZNDZXQPHAUH/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:DMJ2VQBTZTAYQV4ZNDZXQPHAUH","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":"d70f72dc2948a3af62afef120c9aea157ca40012d8ef3597f50ff97efdc84da0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-08T15:25:57Z","title_canon_sha256":"d2590a8b4196f7659be0553226bb62483c0ba030293668236e40b94a13beb059"},"schema_version":"1.0","source":{"id":"1811.03490","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1811.03490","created_at":"2026-05-18T00:01:15Z"},{"alias_kind":"arxiv_version","alias_value":"1811.03490v1","created_at":"2026-05-18T00:01:15Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1811.03490","created_at":"2026-05-18T00:01:15Z"},{"alias_kind":"pith_short_12","alias_value":"DMJ2VQBTZTAY","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"DMJ2VQBTZTAYQV4Z","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"DMJ2VQBT","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:82ddeef0c71acc8f28dbfb8ec58646d3ebda0f8b7de9c288defb722e5e44c0a9","target":"graph","created_at":"2026-05-18T00:01:15Z","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 propose a unified framework for random locations exhibiting some probabilistic symmetries such as stationarity, self-similarity, etc. A theorem of Noether's type is proved, which gives rise to a conservation law describing the change of the density function of a random location as the interval of interest changes. We also discuss the boundary and near boundary behavior of the distributions of the random locations.","authors_text":"Jie Shen, Shunlong Luo, Yi Shen","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-08T15:25:57Z","title":"A Noether theorem for random locations"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1811.03490","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:f5edb9c6d1c5d2d0ed5bcc0627b53a0809ee90637eb07c660e75536113efa2d3","target":"record","created_at":"2026-05-18T00:01:15Z","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":"d70f72dc2948a3af62afef120c9aea157ca40012d8ef3597f50ff97efdc84da0","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-11-08T15:25:57Z","title_canon_sha256":"d2590a8b4196f7659be0553226bb62483c0ba030293668236e40b94a13beb059"},"schema_version":"1.0","source":{"id":"1811.03490","kind":"arxiv","version":1}},"canonical_sha256":"1b13aac033ccc188579968f3783ce0a1c9223223fc62b419c15d37ced0292ed7","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"1b13aac033ccc188579968f3783ce0a1c9223223fc62b419c15d37ced0292ed7","first_computed_at":"2026-05-18T00:01:15.984904Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:01:15.984904Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UjQUL1dinQ7JzowGtXt6xSw6QCXJ1bX687k1QyF8emJ/yFvyWbc0oWSqNSwMkv1NFv9PWvpYGrahEpvs4eJZDA==","signature_status":"signed_v1","signed_at":"2026-05-18T00:01:15.985498Z","signed_message":"canonical_sha256_bytes"},"source_id":"1811.03490","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:f5edb9c6d1c5d2d0ed5bcc0627b53a0809ee90637eb07c660e75536113efa2d3","sha256:82ddeef0c71acc8f28dbfb8ec58646d3ebda0f8b7de9c288defb722e5e44c0a9"],"state_sha256":"e9b2b9d35d2eb3313a6700801c2360af5f2ac183f36d45f1237f4e3f835d20a5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lJ55Yq+MUwdLjZ3JWUQou9KunZVQMWbsg1FGlqfD8Y9FUB1QtMLDtUCZ1loitbU+gnetyTbzlxu1UeEBZ/3UDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-31T23:07:27.931663Z","bundle_sha256":"9ae5302ae8895165134c57cce3be9e6f804b9417fbce0722750e961694b24d4d"}}