{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:WWM45DXPOZC7GEP45WBLCIN5GG","short_pith_number":"pith:WWM45DXP","canonical_record":{"source":{"id":"1102.4265","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-02-21T16:05:10Z","cross_cats_sorted":["astro-ph.CO"],"title_canon_sha256":"eeb17a119a8ad52422d201f6de59ba0989b945c7fb99de21e2668566a2a1bca2","abstract_canon_sha256":"97041254f18739f9df2dfd489a32e381e010bbe14c499574d05ec75704ef52f4"},"schema_version":"1.0"},"canonical_sha256":"b599ce8eef7645f311fced82b121bd318e9556eae5fb8ad9803022b098fdcb1e","source":{"kind":"arxiv","id":"1102.4265","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.4265","created_at":"2026-05-18T02:03:07Z"},{"alias_kind":"arxiv_version","alias_value":"1102.4265v3","created_at":"2026-05-18T02:03:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4265","created_at":"2026-05-18T02:03:07Z"},{"alias_kind":"pith_short_12","alias_value":"WWM45DXPOZC7","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WWM45DXPOZC7GEP4","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WWM45DXP","created_at":"2026-05-18T12:26:44Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:WWM45DXPOZC7GEP45WBLCIN5GG","target":"record","payload":{"canonical_record":{"source":{"id":"1102.4265","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-02-21T16:05:10Z","cross_cats_sorted":["astro-ph.CO"],"title_canon_sha256":"eeb17a119a8ad52422d201f6de59ba0989b945c7fb99de21e2668566a2a1bca2","abstract_canon_sha256":"97041254f18739f9df2dfd489a32e381e010bbe14c499574d05ec75704ef52f4"},"schema_version":"1.0"},"canonical_sha256":"b599ce8eef7645f311fced82b121bd318e9556eae5fb8ad9803022b098fdcb1e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:03:07.008866Z","signature_b64":"jERBFjaY2j2scPP2CfcG3MhlrQvW3CD2kl1xoTeDT9K5cYFUj9KrS7hPhhUZmn/K/UAClCCzohMWt4X9dqtRAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b599ce8eef7645f311fced82b121bd318e9556eae5fb8ad9803022b098fdcb1e","last_reissued_at":"2026-05-18T02:03:07.008271Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:03:07.008271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1102.4265","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":"2026-05-18T02:03:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Y0kjNHf+B6ZIiwmJKszNtX96JAjoyIFJvwM+ivF31jprZv60EDjtaRVDydJa1LIKda0DtMgXlmoXFD28fSRMBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:38:35.870791Z"},"content_sha256":"362b2feb642517bdd5bc0458d2b57ce42b0a14a301acf9aa17b69252b5c5190d","schema_version":"1.0","event_id":"sha256:362b2feb642517bdd5bc0458d2b57ce42b0a14a301acf9aa17b69252b5c5190d"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:WWM45DXPOZC7GEP45WBLCIN5GG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Locally extracting scalar, vector and tensor modes in cosmological perturbation theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO"],"primary_cat":"gr-qc","authors_text":"Bob Osano (University of Cape Town), Chris Clarkson","submitted_at":"2011-02-21T16:05:10Z","abstract_excerpt":"Cosmological perturbation theory relies on the decomposition of perturbations into so-called scalar, vector and tensor modes. This decomposition is non-local and depends on unknowable boundary conditions. The non-locality is particularly important at second- and higher-order because perturbative modes are sourced by products of lower-oder modes, which must be integrated over all space in order to isolate each mode. However, given a trace-free rank-2 tensor, a locally defined scalar mode may be trivially derived by taking two divergences, which knocks out the vector and tensor degrees of freedo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4265","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":""},"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":"2026-05-18T02:03:07Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"xOrvufUcCGEGtMAxOrYysSCEQGn/86eR/EJfL2iaVrs/yQF0+HEeM/mt8xZkhbdiT+5AwjTWedX1THDVd6oGBA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-06T19:38:35.871501Z"},"content_sha256":"e2815f1d03ae1089e08f68cf031be8a5a2be1bf8cb6be4ea72c4d57b89ab6542","schema_version":"1.0","event_id":"sha256:e2815f1d03ae1089e08f68cf031be8a5a2be1bf8cb6be4ea72c4d57b89ab6542"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WWM45DXPOZC7GEP45WBLCIN5GG/bundle.json","state_url":"https://pith.science/pith/WWM45DXPOZC7GEP45WBLCIN5GG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WWM45DXPOZC7GEP45WBLCIN5GG/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":"2026-06-06T19:38:35Z","links":{"resolver":"https://pith.science/pith/WWM45DXPOZC7GEP45WBLCIN5GG","bundle":"https://pith.science/pith/WWM45DXPOZC7GEP45WBLCIN5GG/bundle.json","state":"https://pith.science/pith/WWM45DXPOZC7GEP45WBLCIN5GG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WWM45DXPOZC7GEP45WBLCIN5GG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:WWM45DXPOZC7GEP45WBLCIN5GG","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":"97041254f18739f9df2dfd489a32e381e010bbe14c499574d05ec75704ef52f4","cross_cats_sorted":["astro-ph.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-02-21T16:05:10Z","title_canon_sha256":"eeb17a119a8ad52422d201f6de59ba0989b945c7fb99de21e2668566a2a1bca2"},"schema_version":"1.0","source":{"id":"1102.4265","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1102.4265","created_at":"2026-05-18T02:03:07Z"},{"alias_kind":"arxiv_version","alias_value":"1102.4265v3","created_at":"2026-05-18T02:03:07Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.4265","created_at":"2026-05-18T02:03:07Z"},{"alias_kind":"pith_short_12","alias_value":"WWM45DXPOZC7","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_16","alias_value":"WWM45DXPOZC7GEP4","created_at":"2026-05-18T12:26:44Z"},{"alias_kind":"pith_short_8","alias_value":"WWM45DXP","created_at":"2026-05-18T12:26:44Z"}],"graph_snapshots":[{"event_id":"sha256:e2815f1d03ae1089e08f68cf031be8a5a2be1bf8cb6be4ea72c4d57b89ab6542","target":"graph","created_at":"2026-05-18T02:03:07Z","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":"Cosmological perturbation theory relies on the decomposition of perturbations into so-called scalar, vector and tensor modes. This decomposition is non-local and depends on unknowable boundary conditions. The non-locality is particularly important at second- and higher-order because perturbative modes are sourced by products of lower-oder modes, which must be integrated over all space in order to isolate each mode. However, given a trace-free rank-2 tensor, a locally defined scalar mode may be trivially derived by taking two divergences, which knocks out the vector and tensor degrees of freedo","authors_text":"Bob Osano (University of Cape Town), Chris Clarkson","cross_cats":["astro-ph.CO"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-02-21T16:05:10Z","title":"Locally extracting scalar, vector and tensor modes in cosmological perturbation theory"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.4265","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":"sha256:362b2feb642517bdd5bc0458d2b57ce42b0a14a301acf9aa17b69252b5c5190d","target":"record","created_at":"2026-05-18T02:03:07Z","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":"97041254f18739f9df2dfd489a32e381e010bbe14c499574d05ec75704ef52f4","cross_cats_sorted":["astro-ph.CO"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2011-02-21T16:05:10Z","title_canon_sha256":"eeb17a119a8ad52422d201f6de59ba0989b945c7fb99de21e2668566a2a1bca2"},"schema_version":"1.0","source":{"id":"1102.4265","kind":"arxiv","version":3}},"canonical_sha256":"b599ce8eef7645f311fced82b121bd318e9556eae5fb8ad9803022b098fdcb1e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b599ce8eef7645f311fced82b121bd318e9556eae5fb8ad9803022b098fdcb1e","first_computed_at":"2026-05-18T02:03:07.008271Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:03:07.008271Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"jERBFjaY2j2scPP2CfcG3MhlrQvW3CD2kl1xoTeDT9K5cYFUj9KrS7hPhhUZmn/K/UAClCCzohMWt4X9dqtRAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:03:07.008866Z","signed_message":"canonical_sha256_bytes"},"source_id":"1102.4265","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:362b2feb642517bdd5bc0458d2b57ce42b0a14a301acf9aa17b69252b5c5190d","sha256:e2815f1d03ae1089e08f68cf031be8a5a2be1bf8cb6be4ea72c4d57b89ab6542"],"state_sha256":"ab04015b5285513220f0643a578ca48791bae46fc28691bfa975698f8c25a660"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"meaqLqHrRk8IPzgxAKt3flh/dngiiXA+g5fPa+SpfPsoRmU5nz5sryIIcUMFMUZpXMS3H+VUk1ETqGRUOFNzDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-06T19:38:35.876848Z","bundle_sha256":"00b03c080b5b63b0d3efc227003c031775facd6c1d8fdd90eaa23e435aab964d"}}