{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:73Y7GPYLZMS5QPH6O7DHDZKP34","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":"85ac51f74e5849d6754004a4d039525e81ec7ba961aa5960c27db9c89c611dd8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-08-24T11:37:32Z","title_canon_sha256":"d2ebbe6238092794fa2f1b74b1f953dc943edd055fd3b0abdd34a15d3426a799"},"schema_version":"1.0","source":{"id":"1608.06783","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1608.06783","created_at":"2026-05-18T00:59:19Z"},{"alias_kind":"arxiv_version","alias_value":"1608.06783v1","created_at":"2026-05-18T00:59:19Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1608.06783","created_at":"2026-05-18T00:59:19Z"},{"alias_kind":"pith_short_12","alias_value":"73Y7GPYLZMS5","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_16","alias_value":"73Y7GPYLZMS5QPH6","created_at":"2026-05-18T12:30:04Z"},{"alias_kind":"pith_short_8","alias_value":"73Y7GPYL","created_at":"2026-05-18T12:30:04Z"}],"graph_snapshots":[{"event_id":"sha256:9ad468c7b9a901a79ba6ceb8fd0da83b50d838d01bd0f17641ee3c75e9dba70b","target":"graph","created_at":"2026-05-18T00:59:19Z","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":"Second-order self-force computations, which will be essential in modeling extreme-mass-ratio inspirals, involve two major new difficulties that were not present at first order. One is the problem of large scales, discussed in [Phys. Rev. D 92, 104047 (2015)]. Here we discuss the second difficulty, which occurs instead on small scales: if we expand the field equations in spherical harmonics, then because the first-order field contains a singularity, we require an arbitrarily large number of first-order modes to accurately compute even a single second-order mode. This is a generic feature of non","authors_text":"Adam Pound, Barry Wardell, Jeremy Miller","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-08-24T11:37:32Z","title":"Second-order perturbation theory: the problem of infinite mode coupling"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.06783","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":"sha256:3d0f0b0f1b79731d2e3d47ebb0e19b344121c4dd471b0ed6e87a8dbefdc67c47","target":"record","created_at":"2026-05-18T00:59:19Z","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":"85ac51f74e5849d6754004a4d039525e81ec7ba961aa5960c27db9c89c611dd8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2016-08-24T11:37:32Z","title_canon_sha256":"d2ebbe6238092794fa2f1b74b1f953dc943edd055fd3b0abdd34a15d3426a799"},"schema_version":"1.0","source":{"id":"1608.06783","kind":"arxiv","version":1}},"canonical_sha256":"fef1f33f0bcb25d83cfe77c671e54fdf14c02adff9ac64e303915c7de458f821","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fef1f33f0bcb25d83cfe77c671e54fdf14c02adff9ac64e303915c7de458f821","first_computed_at":"2026-05-18T00:59:19.683454Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:59:19.683454Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TrejY1ATybwjFqW9CvI8vq0lRHzrJGZMZmhht7MGhxjc7GEorXPidQlOWlb+a676UADdF8RcyFFCI+azljRADg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:59:19.684075Z","signed_message":"canonical_sha256_bytes"},"source_id":"1608.06783","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:3d0f0b0f1b79731d2e3d47ebb0e19b344121c4dd471b0ed6e87a8dbefdc67c47","sha256:9ad468c7b9a901a79ba6ceb8fd0da83b50d838d01bd0f17641ee3c75e9dba70b"],"state_sha256":"58cacd87bb193fe82c5bd34e9aa6e13fcf8d7800374b55bc62b4da8132342286"}