{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:CDGL7NJYZRIICWQGH6Z7VOD3VK","short_pith_number":"pith:CDGL7NJY","canonical_record":{"source":{"id":"1710.10185","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2017-10-24T03:13:53Z","cross_cats_sorted":[],"title_canon_sha256":"dcf425c31a809418df6cea63b62609986f84aa51ac843b8a9bda1d265b9e9d0e","abstract_canon_sha256":"51eda45072e4263191090361d58fbaf2064a83df5472b374e2e84e53e87c5290"},"schema_version":"1.0"},"canonical_sha256":"10ccbfb538cc50815a063fb3fab87baaba781f9262e4e64eb9dc7b49634927f3","source":{"kind":"arxiv","id":"1710.10185","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.10185","created_at":"2026-05-18T00:30:40Z"},{"alias_kind":"arxiv_version","alias_value":"1710.10185v2","created_at":"2026-05-18T00:30:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.10185","created_at":"2026-05-18T00:30:40Z"},{"alias_kind":"pith_short_12","alias_value":"CDGL7NJYZRII","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CDGL7NJYZRIICWQG","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CDGL7NJY","created_at":"2026-05-18T12:31:10Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:CDGL7NJYZRIICWQGH6Z7VOD3VK","target":"record","payload":{"canonical_record":{"source":{"id":"1710.10185","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2017-10-24T03:13:53Z","cross_cats_sorted":[],"title_canon_sha256":"dcf425c31a809418df6cea63b62609986f84aa51ac843b8a9bda1d265b9e9d0e","abstract_canon_sha256":"51eda45072e4263191090361d58fbaf2064a83df5472b374e2e84e53e87c5290"},"schema_version":"1.0"},"canonical_sha256":"10ccbfb538cc50815a063fb3fab87baaba781f9262e4e64eb9dc7b49634927f3","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:30:40.403563Z","signature_b64":"h2Bzb0nOqotGtvSXV5i/E2FeTIz2zPB2T655CjtWxgLioPNfwaZ6m0YKgqSiivf+gVOYLpPFJ3L7qOvEqtkjBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"10ccbfb538cc50815a063fb3fab87baaba781f9262e4e64eb9dc7b49634927f3","last_reissued_at":"2026-05-18T00:30:40.402922Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:30:40.402922Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.10185","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":"2026-05-18T00:30:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YnM8QKoKCPCCJ/Tf/oHruDt4HgrN6S0/5ybKkMnwQI+UzSLyNcu0lW3bNbJK/Pq1JuzNpc4vLMnmUG6VPRi9CQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T05:00:42.734891Z"},"content_sha256":"6b06e83055f6cb1ba56de2628f3c18683692fe207602f4712e45d931b74f38c2","schema_version":"1.0","event_id":"sha256:6b06e83055f6cb1ba56de2628f3c18683692fe207602f4712e45d931b74f38c2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:CDGL7NJYZRIICWQGH6Z7VOD3VK","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Large scale density perturbations from a uniform distribution by wave transport","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"astro-ph.CO","authors_text":"Richard Lieu","submitted_at":"2017-10-24T03:13:53Z","abstract_excerpt":"It has long been known that a uniform distribution of matter cannot produce a Poisson distribution of density fluctuations on very large scales $1/k > ct$ by the motion of discrete particles over timescale $t$. The constraint is part of what is sometimes referred to as the Zel'dovich bound. We investigate in this paper the transport of energy by the propagation of waves emanating {\\it incoherently} from a regular and infinite lattice of oscillators, each having the same finite amount of energy reserve initially. The model we employ does not involve the expansion of the Universe -- the scales o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10185","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":"2026-05-18T00:30:40Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"C+Yfv6AJvEYYNqWzJaKtgmMWNOkWwb4sDf0T4vKBKNg9Hh9jJWdHVdIXETcz3WDvcrEurLKXtL6F9NfBwHK+Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-10T05:00:42.735707Z"},"content_sha256":"7fa2c8bb7e6b59e08297287aa2cb6f03b2fb2eb20af570244feeeed19abd4e77","schema_version":"1.0","event_id":"sha256:7fa2c8bb7e6b59e08297287aa2cb6f03b2fb2eb20af570244feeeed19abd4e77"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/CDGL7NJYZRIICWQGH6Z7VOD3VK/bundle.json","state_url":"https://pith.science/pith/CDGL7NJYZRIICWQGH6Z7VOD3VK/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/CDGL7NJYZRIICWQGH6Z7VOD3VK/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":"2026-06-10T05:00:42Z","links":{"resolver":"https://pith.science/pith/CDGL7NJYZRIICWQGH6Z7VOD3VK","bundle":"https://pith.science/pith/CDGL7NJYZRIICWQGH6Z7VOD3VK/bundle.json","state":"https://pith.science/pith/CDGL7NJYZRIICWQGH6Z7VOD3VK/state.json","well_known_bundle":"https://pith.science/.well-known/pith/CDGL7NJYZRIICWQGH6Z7VOD3VK/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:CDGL7NJYZRIICWQGH6Z7VOD3VK","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":"51eda45072e4263191090361d58fbaf2064a83df5472b374e2e84e53e87c5290","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2017-10-24T03:13:53Z","title_canon_sha256":"dcf425c31a809418df6cea63b62609986f84aa51ac843b8a9bda1d265b9e9d0e"},"schema_version":"1.0","source":{"id":"1710.10185","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.10185","created_at":"2026-05-18T00:30:40Z"},{"alias_kind":"arxiv_version","alias_value":"1710.10185v2","created_at":"2026-05-18T00:30:40Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.10185","created_at":"2026-05-18T00:30:40Z"},{"alias_kind":"pith_short_12","alias_value":"CDGL7NJYZRII","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_16","alias_value":"CDGL7NJYZRIICWQG","created_at":"2026-05-18T12:31:10Z"},{"alias_kind":"pith_short_8","alias_value":"CDGL7NJY","created_at":"2026-05-18T12:31:10Z"}],"graph_snapshots":[{"event_id":"sha256:7fa2c8bb7e6b59e08297287aa2cb6f03b2fb2eb20af570244feeeed19abd4e77","target":"graph","created_at":"2026-05-18T00:30:40Z","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":"It has long been known that a uniform distribution of matter cannot produce a Poisson distribution of density fluctuations on very large scales $1/k > ct$ by the motion of discrete particles over timescale $t$. The constraint is part of what is sometimes referred to as the Zel'dovich bound. We investigate in this paper the transport of energy by the propagation of waves emanating {\\it incoherently} from a regular and infinite lattice of oscillators, each having the same finite amount of energy reserve initially. The model we employ does not involve the expansion of the Universe -- the scales o","authors_text":"Richard Lieu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2017-10-24T03:13:53Z","title":"Large scale density perturbations from a uniform distribution by wave transport"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.10185","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":"sha256:6b06e83055f6cb1ba56de2628f3c18683692fe207602f4712e45d931b74f38c2","target":"record","created_at":"2026-05-18T00:30:40Z","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":"51eda45072e4263191090361d58fbaf2064a83df5472b374e2e84e53e87c5290","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2017-10-24T03:13:53Z","title_canon_sha256":"dcf425c31a809418df6cea63b62609986f84aa51ac843b8a9bda1d265b9e9d0e"},"schema_version":"1.0","source":{"id":"1710.10185","kind":"arxiv","version":2}},"canonical_sha256":"10ccbfb538cc50815a063fb3fab87baaba781f9262e4e64eb9dc7b49634927f3","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"10ccbfb538cc50815a063fb3fab87baaba781f9262e4e64eb9dc7b49634927f3","first_computed_at":"2026-05-18T00:30:40.402922Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:30:40.402922Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h2Bzb0nOqotGtvSXV5i/E2FeTIz2zPB2T655CjtWxgLioPNfwaZ6m0YKgqSiivf+gVOYLpPFJ3L7qOvEqtkjBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:30:40.403563Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.10185","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6b06e83055f6cb1ba56de2628f3c18683692fe207602f4712e45d931b74f38c2","sha256:7fa2c8bb7e6b59e08297287aa2cb6f03b2fb2eb20af570244feeeed19abd4e77"],"state_sha256":"aa8fe3b8965d478fa67c7c72cb69ab3fdf1ca818e2ea54fe8efe60430bd6d2c6"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"b07o8hV+c4HlqjBo4avUVxjUteP3f7PhhCliRE2Hrgn/jRD8ONt46WSt6BZY4IFWX01h0TdB2+tP3JtRKhGKCQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-10T05:00:42.739595Z","bundle_sha256":"9e13272331b1c540fcd3157d430619b4ce1d1fb3d11f5b2b7659a566dd561168"}}