{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2016:I3TGO7JEHTEOHQEI2ZKCHZF6TO","short_pith_number":"pith:I3TGO7JE","canonical_record":{"source":{"id":"1605.09417","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2016-05-30T21:12:48Z","cross_cats_sorted":["gr-qc","hep-ph"],"title_canon_sha256":"606d87409a7fe919c2fcc41a235e2c7103183817f84cdf9aacd146223cf74fde","abstract_canon_sha256":"65307934826195deed60cd705d8f94990207e7bc45e61565d9cf238c35a4ce3b"},"schema_version":"1.0"},"canonical_sha256":"46e6677d243cc8e3c088d65423e4be9b9d1cb8aff19317bfae25e1889aacba51","source":{"kind":"arxiv","id":"1605.09417","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.09417","created_at":"2026-05-18T01:13:17Z"},{"alias_kind":"arxiv_version","alias_value":"1605.09417v1","created_at":"2026-05-18T01:13:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.09417","created_at":"2026-05-18T01:13:17Z"},{"alias_kind":"pith_short_12","alias_value":"I3TGO7JEHTEO","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"I3TGO7JEHTEOHQEI","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"I3TGO7JE","created_at":"2026-05-18T12:30:22Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2016:I3TGO7JEHTEOHQEI2ZKCHZF6TO","target":"record","payload":{"canonical_record":{"source":{"id":"1605.09417","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2016-05-30T21:12:48Z","cross_cats_sorted":["gr-qc","hep-ph"],"title_canon_sha256":"606d87409a7fe919c2fcc41a235e2c7103183817f84cdf9aacd146223cf74fde","abstract_canon_sha256":"65307934826195deed60cd705d8f94990207e7bc45e61565d9cf238c35a4ce3b"},"schema_version":"1.0"},"canonical_sha256":"46e6677d243cc8e3c088d65423e4be9b9d1cb8aff19317bfae25e1889aacba51","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:13:17.380665Z","signature_b64":"52Y6rnfOoLv5z1m1DOGQkt2xL3IM3pAyDWzjjhJk0BmzyINX4BU6l1VSlfxu8TOhxwUsacP4zT5bdoVNpkWeBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"46e6677d243cc8e3c088d65423e4be9b9d1cb8aff19317bfae25e1889aacba51","last_reissued_at":"2026-05-18T01:13:17.380272Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:13:17.380272Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1605.09417","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":"2026-05-18T01:13:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0kqnivWZXNvAMHEbjpHfcIOcYudSjF/BfRbHBYWedfMoHkL4lr3JfLs0VpK0mgpfS9SPnLnTztuDu56A8kT6DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:22:03.966845Z"},"content_sha256":"6c1d35c235d2cdbb3ec997e8fb10461bb7789bfb79bef4b9772328c448c81565","schema_version":"1.0","event_id":"sha256:6c1d35c235d2cdbb3ec997e8fb10461bb7789bfb79bef4b9772328c448c81565"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2016:I3TGO7JEHTEOHQEI2ZKCHZF6TO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Massive neutrinos in nonlinear large scale structure: A consistent perturbation theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["gr-qc","hep-ph"],"primary_cat":"astro-ph.CO","authors_text":"Michele Levi, Zvonimir Vlah","submitted_at":"2016-05-30T21:12:48Z","abstract_excerpt":"A consistent formulation to incorporate massive neutrinos in the perturbation theory of the effective CDM+baryons fluid is introduced. In this formulation all linear k dependence in the growth functions of CDM+baryons perturbations, as well as all consequent additional mode coupling at higher orders, are taken into account to any desirable accuracy. Our formulation regards the neutrino fraction, which is constant in time after the non-relativistic transition of neutrinos, and much smaller than unity, as the coupling constant of the theory. Then the \"bare\" perturbations are those in the massles"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.09417","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":"2026-05-18T01:13:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"+iUXN6moZyZx5OT71zATZgrpit7dYt9G/A+LG6BtyZm5GGu1mcBvXCgd/ySfWW8bqnq9hgxWKPjNDvzYVT+SBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-05-26T20:22:03.967535Z"},"content_sha256":"17abb97cf1ca52907ab3edbea07c076faf827d34cf24ff1499232a4944166dc3","schema_version":"1.0","event_id":"sha256:17abb97cf1ca52907ab3edbea07c076faf827d34cf24ff1499232a4944166dc3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/I3TGO7JEHTEOHQEI2ZKCHZF6TO/bundle.json","state_url":"https://pith.science/pith/I3TGO7JEHTEOHQEI2ZKCHZF6TO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/I3TGO7JEHTEOHQEI2ZKCHZF6TO/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":"2026-05-26T20:22:03Z","links":{"resolver":"https://pith.science/pith/I3TGO7JEHTEOHQEI2ZKCHZF6TO","bundle":"https://pith.science/pith/I3TGO7JEHTEOHQEI2ZKCHZF6TO/bundle.json","state":"https://pith.science/pith/I3TGO7JEHTEOHQEI2ZKCHZF6TO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/I3TGO7JEHTEOHQEI2ZKCHZF6TO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:I3TGO7JEHTEOHQEI2ZKCHZF6TO","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":"65307934826195deed60cd705d8f94990207e7bc45e61565d9cf238c35a4ce3b","cross_cats_sorted":["gr-qc","hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2016-05-30T21:12:48Z","title_canon_sha256":"606d87409a7fe919c2fcc41a235e2c7103183817f84cdf9aacd146223cf74fde"},"schema_version":"1.0","source":{"id":"1605.09417","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1605.09417","created_at":"2026-05-18T01:13:17Z"},{"alias_kind":"arxiv_version","alias_value":"1605.09417v1","created_at":"2026-05-18T01:13:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.09417","created_at":"2026-05-18T01:13:17Z"},{"alias_kind":"pith_short_12","alias_value":"I3TGO7JEHTEO","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_16","alias_value":"I3TGO7JEHTEOHQEI","created_at":"2026-05-18T12:30:22Z"},{"alias_kind":"pith_short_8","alias_value":"I3TGO7JE","created_at":"2026-05-18T12:30:22Z"}],"graph_snapshots":[{"event_id":"sha256:17abb97cf1ca52907ab3edbea07c076faf827d34cf24ff1499232a4944166dc3","target":"graph","created_at":"2026-05-18T01:13:17Z","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":"A consistent formulation to incorporate massive neutrinos in the perturbation theory of the effective CDM+baryons fluid is introduced. In this formulation all linear k dependence in the growth functions of CDM+baryons perturbations, as well as all consequent additional mode coupling at higher orders, are taken into account to any desirable accuracy. Our formulation regards the neutrino fraction, which is constant in time after the non-relativistic transition of neutrinos, and much smaller than unity, as the coupling constant of the theory. Then the \"bare\" perturbations are those in the massles","authors_text":"Michele Levi, Zvonimir Vlah","cross_cats":["gr-qc","hep-ph"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2016-05-30T21:12:48Z","title":"Massive neutrinos in nonlinear large scale structure: A consistent perturbation theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.09417","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":"sha256:6c1d35c235d2cdbb3ec997e8fb10461bb7789bfb79bef4b9772328c448c81565","target":"record","created_at":"2026-05-18T01:13:17Z","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":"65307934826195deed60cd705d8f94990207e7bc45e61565d9cf238c35a4ce3b","cross_cats_sorted":["gr-qc","hep-ph"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"astro-ph.CO","submitted_at":"2016-05-30T21:12:48Z","title_canon_sha256":"606d87409a7fe919c2fcc41a235e2c7103183817f84cdf9aacd146223cf74fde"},"schema_version":"1.0","source":{"id":"1605.09417","kind":"arxiv","version":1}},"canonical_sha256":"46e6677d243cc8e3c088d65423e4be9b9d1cb8aff19317bfae25e1889aacba51","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"46e6677d243cc8e3c088d65423e4be9b9d1cb8aff19317bfae25e1889aacba51","first_computed_at":"2026-05-18T01:13:17.380272Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:13:17.380272Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"52Y6rnfOoLv5z1m1DOGQkt2xL3IM3pAyDWzjjhJk0BmzyINX4BU6l1VSlfxu8TOhxwUsacP4zT5bdoVNpkWeBA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:13:17.380665Z","signed_message":"canonical_sha256_bytes"},"source_id":"1605.09417","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6c1d35c235d2cdbb3ec997e8fb10461bb7789bfb79bef4b9772328c448c81565","sha256:17abb97cf1ca52907ab3edbea07c076faf827d34cf24ff1499232a4944166dc3"],"state_sha256":"1c37d337b23e72f13d434f2512a288d0075d03ed91bf0e402f4b86d246fa63c0"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"oQi1LTquljVX7MR94evAauyDJAI5PNavoqokSQdj+QmGvmzccLNZGJ3MMU3WPz+UkAjGIPlavq3Jcnvxy8NNAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-05-26T20:22:03.970819Z","bundle_sha256":"3247a69f3efeb0606a616ed8a9c75b75c78f04c04bbf1d0165cc4815682732d8"}}