{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:5P3JFNLVGASFQUEOYDLIZDTZNY","short_pith_number":"pith:5P3JFNLV","canonical_record":{"source":{"id":"1810.07957","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-10-18T09:19:09Z","cross_cats_sorted":["astro-ph.CO","hep-ph","hep-th"],"title_canon_sha256":"72c1a0bb20a354baa6f569defb8f4a535c562887c5eb3f9975d18cd6df6b3c5a","abstract_canon_sha256":"e42f5929a18fceec9cbf4d2c36f26c6efd06225eb1a9f8700e5443d2dcfe3032"},"schema_version":"1.0"},"canonical_sha256":"ebf692b575302458508ec0d68c8e796e0dee1573eb48ae4e187ead67d7ae205d","source":{"kind":"arxiv","id":"1810.07957","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.07957","created_at":"2026-05-17T23:57:31Z"},{"alias_kind":"arxiv_version","alias_value":"1810.07957v2","created_at":"2026-05-17T23:57:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.07957","created_at":"2026-05-17T23:57:31Z"},{"alias_kind":"pith_short_12","alias_value":"5P3JFNLVGASF","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5P3JFNLVGASFQUEO","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5P3JFNLV","created_at":"2026-05-18T12:32:08Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:5P3JFNLVGASFQUEOYDLIZDTZNY","target":"record","payload":{"canonical_record":{"source":{"id":"1810.07957","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-10-18T09:19:09Z","cross_cats_sorted":["astro-ph.CO","hep-ph","hep-th"],"title_canon_sha256":"72c1a0bb20a354baa6f569defb8f4a535c562887c5eb3f9975d18cd6df6b3c5a","abstract_canon_sha256":"e42f5929a18fceec9cbf4d2c36f26c6efd06225eb1a9f8700e5443d2dcfe3032"},"schema_version":"1.0"},"canonical_sha256":"ebf692b575302458508ec0d68c8e796e0dee1573eb48ae4e187ead67d7ae205d","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:57:31.048178Z","signature_b64":"VM2nmtZ2av3AwkBOpN+48vlUO6uCmXPJ/UR1tFnC1qRrVQo7zGio1MB/qcoyZEwfM2zkxU1EulWcfIpmfbQWCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ebf692b575302458508ec0d68c8e796e0dee1573eb48ae4e187ead67d7ae205d","last_reissued_at":"2026-05-17T23:57:31.047603Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:57:31.047603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1810.07957","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":"2026-05-17T23:57:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZZqpc4a3hEJyVYmaBgNn4NA2sIN6Z/XPexZqkjsS2KWXmESE6NzxrfDavt3gGRI5b/38+6I7om4YtsfVQSJ4Dw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:47:33.259239Z"},"content_sha256":"538c823d65482fe59727c5cd9cd6200b9b066e483eb56bb18f6b160253cacc2f","schema_version":"1.0","event_id":"sha256:538c823d65482fe59727c5cd9cd6200b9b066e483eb56bb18f6b160253cacc2f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:5P3JFNLVGASFQUEOYDLIZDTZNY","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Most general cubic-order Horndeski Lagrangian allowing for scaling solutions and the application to dark energy","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","hep-ph","hep-th"],"primary_cat":"gr-qc","authors_text":"Nelson J. Nunes, Noemi Frusciante, Ryotaro Kase, Shinji Tsujikawa","submitted_at":"2018-10-18T09:19:09Z","abstract_excerpt":"In cubic-order Horndeski theories where a scalar field $\\phi$ is coupled to nonrelativistic matter with a field-dependent coupling $Q(\\phi)$, we derive the most general Lagrangian having scaling solutions on the isotropic and homogenous cosmological background. For constant $Q$ including the case of vanishing coupling, the corresponding Lagrangian reduces to the form $L=Xg_2(Y)-g_3(Y)\\square \\phi$, where $X=-\\partial_{\\mu}\\phi\\partial^{\\mu}\\phi/2$ and $g_2, g_3$ are arbitrary functions of $Y=Xe^{\\lambda \\phi}$ with constant $\\lambda$. We obtain the fixed points of the scaling Lagrangian for co"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.07957","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":"2026-05-17T23:57:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"YrLYK1hAszsdGhvi4iuObEykSWORp6MSdZjBefPf4UkQAenV5HGiQ6ZnnH36Frp/CjO9RjuaLYVMlFYn0U/PDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-04T06:47:33.259879Z"},"content_sha256":"4af01f16b7a0f0a79a2287393ac791f4f209688a37f6ac588d5e53c33c5276c3","schema_version":"1.0","event_id":"sha256:4af01f16b7a0f0a79a2287393ac791f4f209688a37f6ac588d5e53c33c5276c3"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/5P3JFNLVGASFQUEOYDLIZDTZNY/bundle.json","state_url":"https://pith.science/pith/5P3JFNLVGASFQUEOYDLIZDTZNY/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/5P3JFNLVGASFQUEOYDLIZDTZNY/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":"2026-06-04T06:47:33Z","links":{"resolver":"https://pith.science/pith/5P3JFNLVGASFQUEOYDLIZDTZNY","bundle":"https://pith.science/pith/5P3JFNLVGASFQUEOYDLIZDTZNY/bundle.json","state":"https://pith.science/pith/5P3JFNLVGASFQUEOYDLIZDTZNY/state.json","well_known_bundle":"https://pith.science/.well-known/pith/5P3JFNLVGASFQUEOYDLIZDTZNY/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:5P3JFNLVGASFQUEOYDLIZDTZNY","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":"e42f5929a18fceec9cbf4d2c36f26c6efd06225eb1a9f8700e5443d2dcfe3032","cross_cats_sorted":["astro-ph.CO","hep-ph","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-10-18T09:19:09Z","title_canon_sha256":"72c1a0bb20a354baa6f569defb8f4a535c562887c5eb3f9975d18cd6df6b3c5a"},"schema_version":"1.0","source":{"id":"1810.07957","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1810.07957","created_at":"2026-05-17T23:57:31Z"},{"alias_kind":"arxiv_version","alias_value":"1810.07957v2","created_at":"2026-05-17T23:57:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.07957","created_at":"2026-05-17T23:57:31Z"},{"alias_kind":"pith_short_12","alias_value":"5P3JFNLVGASF","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_16","alias_value":"5P3JFNLVGASFQUEO","created_at":"2026-05-18T12:32:08Z"},{"alias_kind":"pith_short_8","alias_value":"5P3JFNLV","created_at":"2026-05-18T12:32:08Z"}],"graph_snapshots":[{"event_id":"sha256:4af01f16b7a0f0a79a2287393ac791f4f209688a37f6ac588d5e53c33c5276c3","target":"graph","created_at":"2026-05-17T23:57:31Z","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":"In cubic-order Horndeski theories where a scalar field $\\phi$ is coupled to nonrelativistic matter with a field-dependent coupling $Q(\\phi)$, we derive the most general Lagrangian having scaling solutions on the isotropic and homogenous cosmological background. For constant $Q$ including the case of vanishing coupling, the corresponding Lagrangian reduces to the form $L=Xg_2(Y)-g_3(Y)\\square \\phi$, where $X=-\\partial_{\\mu}\\phi\\partial^{\\mu}\\phi/2$ and $g_2, g_3$ are arbitrary functions of $Y=Xe^{\\lambda \\phi}$ with constant $\\lambda$. We obtain the fixed points of the scaling Lagrangian for co","authors_text":"Nelson J. Nunes, Noemi Frusciante, Ryotaro Kase, Shinji Tsujikawa","cross_cats":["astro-ph.CO","hep-ph","hep-th"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-10-18T09:19:09Z","title":"Most general cubic-order Horndeski Lagrangian allowing for scaling solutions and the application to dark energy"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.07957","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":"sha256:538c823d65482fe59727c5cd9cd6200b9b066e483eb56bb18f6b160253cacc2f","target":"record","created_at":"2026-05-17T23:57:31Z","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":"e42f5929a18fceec9cbf4d2c36f26c6efd06225eb1a9f8700e5443d2dcfe3032","cross_cats_sorted":["astro-ph.CO","hep-ph","hep-th"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-10-18T09:19:09Z","title_canon_sha256":"72c1a0bb20a354baa6f569defb8f4a535c562887c5eb3f9975d18cd6df6b3c5a"},"schema_version":"1.0","source":{"id":"1810.07957","kind":"arxiv","version":2}},"canonical_sha256":"ebf692b575302458508ec0d68c8e796e0dee1573eb48ae4e187ead67d7ae205d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ebf692b575302458508ec0d68c8e796e0dee1573eb48ae4e187ead67d7ae205d","first_computed_at":"2026-05-17T23:57:31.047603Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:57:31.047603Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"VM2nmtZ2av3AwkBOpN+48vlUO6uCmXPJ/UR1tFnC1qRrVQo7zGio1MB/qcoyZEwfM2zkxU1EulWcfIpmfbQWCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:57:31.048178Z","signed_message":"canonical_sha256_bytes"},"source_id":"1810.07957","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:538c823d65482fe59727c5cd9cd6200b9b066e483eb56bb18f6b160253cacc2f","sha256:4af01f16b7a0f0a79a2287393ac791f4f209688a37f6ac588d5e53c33c5276c3"],"state_sha256":"d0b4fbc6a0c9b13031e8ccfcbee3470d04d7c2681499a58c5c0fe93839e220b1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"q6SSd3AtSo/uF3PR+ekbs3akkm8RWpcHBKhrZAMPDq7U/ZZyqXurcVhvX0dwV6FqUdNMlGzKODCGsRxrkfNtAw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-04T06:47:33.262994Z","bundle_sha256":"2449b445d06e9821f9bf8cd7108fc20cc361b88f862869376036c9e34865c634"}}