{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:BP4Q5EJZCQBQVLNUPPR4WM44VO","short_pith_number":"pith:BP4Q5EJZ","canonical_record":{"source":{"id":"1809.09633","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-09-25T18:00:11Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"8cadcddceb304e71c37d5a69aeb9988053e21c7db97f58aa8b7da24f3c76d353","abstract_canon_sha256":"7c2a8e312db5fcc3bfb2e5965110006694f98ac73ea00f58ee9145b1f5d07bb0"},"schema_version":"1.0"},"canonical_sha256":"0bf90e913914030aadb47be3cb339cabba499cba0367fb44bdae682580f22b7e","source":{"kind":"arxiv","id":"1809.09633","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.09633","created_at":"2026-05-17T23:51:05Z"},{"alias_kind":"arxiv_version","alias_value":"1809.09633v3","created_at":"2026-05-17T23:51:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.09633","created_at":"2026-05-17T23:51:05Z"},{"alias_kind":"pith_short_12","alias_value":"BP4Q5EJZCQBQ","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BP4Q5EJZCQBQVLNU","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BP4Q5EJZ","created_at":"2026-05-18T12:32:16Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:BP4Q5EJZCQBQVLNUPPR4WM44VO","target":"record","payload":{"canonical_record":{"source":{"id":"1809.09633","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-09-25T18:00:11Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"8cadcddceb304e71c37d5a69aeb9988053e21c7db97f58aa8b7da24f3c76d353","abstract_canon_sha256":"7c2a8e312db5fcc3bfb2e5965110006694f98ac73ea00f58ee9145b1f5d07bb0"},"schema_version":"1.0"},"canonical_sha256":"0bf90e913914030aadb47be3cb339cabba499cba0367fb44bdae682580f22b7e","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:51:05.469772Z","signature_b64":"CAnb2+d8ale+scYlevOdH4i+q5ZdiNbOk8jfSbQnF8N15pbo3rFlzDv6LmKqSlHIlbPhw4y2tokdXbw0plB4Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"0bf90e913914030aadb47be3cb339cabba499cba0367fb44bdae682580f22b7e","last_reissued_at":"2026-05-17T23:51:05.469288Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:51:05.469288Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1809.09633","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":"2026-05-17T23:51:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I1qgW+noFFfCsngluzsPqR0fMHxm9bgvZQGEF+dw6vwOc5t/FFl6Gi8wMwPxi3Z7zTe3rilFzzPaFwsixoVqCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T19:25:11.420002Z"},"content_sha256":"60a4b261a1404c8e6a5b04a05d88ea8de1c4485036212ac74b159fcebcb9bfc2","schema_version":"1.0","event_id":"sha256:60a4b261a1404c8e6a5b04a05d88ea8de1c4485036212ac74b159fcebcb9bfc2"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:BP4Q5EJZCQBQVLNUPPR4WM44VO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Solutions of the wave equation bounded at the Big Bang","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"gr-qc","authors_text":"Jorge Drumond Silva, Jos\\'e Nat\\'ario, Pedro M. Gir\\~ao","submitted_at":"2018-09-25T18:00:11Z","abstract_excerpt":"By solving a singular initial value problem, we prove the existence of solutions of the wave equation $\\Box_g\\phi=0$ which are bounded at the Big Bang in the Friedmann-Lemaitre-Robertson-Walker cosmological models. More precisely, we show that given any function $A \\in H^3(\\Sigma)$ (where $\\Sigma=\\mathbb{R}^n, \\mathbb{S}^n$ or $\\mathbb{H}^n$ models the spatial hypersurfaces) there exists a unique solution $\\phi$ of the wave equation converging to $A$ in $H^1(\\Sigma)$ at the Big Bang, and whose time derivative is suitably controlled in $L^2(\\Sigma)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.09633","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":"2026-05-17T23:51:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"K7xm3u4bddfMnra0i2w4yVQZmD9Y/Myl3eWuDG0wzqPROcTSd4y7eDX9YjOBDT4V+/O1jTCn0zyq0EP/WCcMCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T19:25:11.420355Z"},"content_sha256":"19655daa8d590a44d165e4400e5a102c9c1cf9810d31320289e5e6ee05a5a6e9","schema_version":"1.0","event_id":"sha256:19655daa8d590a44d165e4400e5a102c9c1cf9810d31320289e5e6ee05a5a6e9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/BP4Q5EJZCQBQVLNUPPR4WM44VO/bundle.json","state_url":"https://pith.science/pith/BP4Q5EJZCQBQVLNUPPR4WM44VO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/BP4Q5EJZCQBQVLNUPPR4WM44VO/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":"2026-06-24T19:25:11Z","links":{"resolver":"https://pith.science/pith/BP4Q5EJZCQBQVLNUPPR4WM44VO","bundle":"https://pith.science/pith/BP4Q5EJZCQBQVLNUPPR4WM44VO/bundle.json","state":"https://pith.science/pith/BP4Q5EJZCQBQVLNUPPR4WM44VO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/BP4Q5EJZCQBQVLNUPPR4WM44VO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:BP4Q5EJZCQBQVLNUPPR4WM44VO","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":"7c2a8e312db5fcc3bfb2e5965110006694f98ac73ea00f58ee9145b1f5d07bb0","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-09-25T18:00:11Z","title_canon_sha256":"8cadcddceb304e71c37d5a69aeb9988053e21c7db97f58aa8b7da24f3c76d353"},"schema_version":"1.0","source":{"id":"1809.09633","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1809.09633","created_at":"2026-05-17T23:51:05Z"},{"alias_kind":"arxiv_version","alias_value":"1809.09633v3","created_at":"2026-05-17T23:51:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1809.09633","created_at":"2026-05-17T23:51:05Z"},{"alias_kind":"pith_short_12","alias_value":"BP4Q5EJZCQBQ","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_16","alias_value":"BP4Q5EJZCQBQVLNU","created_at":"2026-05-18T12:32:16Z"},{"alias_kind":"pith_short_8","alias_value":"BP4Q5EJZ","created_at":"2026-05-18T12:32:16Z"}],"graph_snapshots":[{"event_id":"sha256:19655daa8d590a44d165e4400e5a102c9c1cf9810d31320289e5e6ee05a5a6e9","target":"graph","created_at":"2026-05-17T23:51:05Z","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":"By solving a singular initial value problem, we prove the existence of solutions of the wave equation $\\Box_g\\phi=0$ which are bounded at the Big Bang in the Friedmann-Lemaitre-Robertson-Walker cosmological models. More precisely, we show that given any function $A \\in H^3(\\Sigma)$ (where $\\Sigma=\\mathbb{R}^n, \\mathbb{S}^n$ or $\\mathbb{H}^n$ models the spatial hypersurfaces) there exists a unique solution $\\phi$ of the wave equation converging to $A$ in $H^1(\\Sigma)$ at the Big Bang, and whose time derivative is suitably controlled in $L^2(\\Sigma)$.","authors_text":"Jorge Drumond Silva, Jos\\'e Nat\\'ario, Pedro M. Gir\\~ao","cross_cats":["math-ph","math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-09-25T18:00:11Z","title":"Solutions of the wave equation bounded at the Big Bang"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.09633","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":"sha256:60a4b261a1404c8e6a5b04a05d88ea8de1c4485036212ac74b159fcebcb9bfc2","target":"record","created_at":"2026-05-17T23:51:05Z","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":"7c2a8e312db5fcc3bfb2e5965110006694f98ac73ea00f58ee9145b1f5d07bb0","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-09-25T18:00:11Z","title_canon_sha256":"8cadcddceb304e71c37d5a69aeb9988053e21c7db97f58aa8b7da24f3c76d353"},"schema_version":"1.0","source":{"id":"1809.09633","kind":"arxiv","version":3}},"canonical_sha256":"0bf90e913914030aadb47be3cb339cabba499cba0367fb44bdae682580f22b7e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"0bf90e913914030aadb47be3cb339cabba499cba0367fb44bdae682580f22b7e","first_computed_at":"2026-05-17T23:51:05.469288Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:51:05.469288Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"CAnb2+d8ale+scYlevOdH4i+q5ZdiNbOk8jfSbQnF8N15pbo3rFlzDv6LmKqSlHIlbPhw4y2tokdXbw0plB4Cg==","signature_status":"signed_v1","signed_at":"2026-05-17T23:51:05.469772Z","signed_message":"canonical_sha256_bytes"},"source_id":"1809.09633","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:60a4b261a1404c8e6a5b04a05d88ea8de1c4485036212ac74b159fcebcb9bfc2","sha256:19655daa8d590a44d165e4400e5a102c9c1cf9810d31320289e5e6ee05a5a6e9"],"state_sha256":"4abafd75b25eca56d4d6e28a90aaf1834992cabf247b13fad8f0ed4698041b58"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"QvkTWmrqrM8yU91xy75EberZCV7Fp44uWi5gTO+BjlA4eZwZQp9BtBWJGm5jflv95R6OdZhEoYhPul8QDmzNBQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T19:25:11.422251Z","bundle_sha256":"12d11a5cab31aa31f47f7d9aa8e0f295dfe28bc077ba259de38721a6d4d8b7bb"}}