{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2015:Z3DGC43MPNUWIE5PHPBJP2NBXW","short_pith_number":"pith:Z3DGC43M","canonical_record":{"source":{"id":"1512.05434","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-12-17T01:27:51Z","cross_cats_sorted":["astro-ph.CO","hep-th","math-ph","math.MP"],"title_canon_sha256":"c389bc1a5db69d1522eb29ba3728fdd77ffd4ef9cba3d525f630c8bc71fad119","abstract_canon_sha256":"df05f33551b8db6b1d90bb7974fa9f86b65c373b85f8df91b637cc748a32eb75"},"schema_version":"1.0"},"canonical_sha256":"cec661736c7b696413af3bc297e9a1bdb43586ede6774cf0907a05a13c70475a","source":{"kind":"arxiv","id":"1512.05434","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.05434","created_at":"2026-05-18T01:23:33Z"},{"alias_kind":"arxiv_version","alias_value":"1512.05434v1","created_at":"2026-05-18T01:23:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.05434","created_at":"2026-05-18T01:23:33Z"},{"alias_kind":"pith_short_12","alias_value":"Z3DGC43MPNUW","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"Z3DGC43MPNUWIE5P","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"Z3DGC43M","created_at":"2026-05-18T12:29:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2015:Z3DGC43MPNUWIE5PHPBJP2NBXW","target":"record","payload":{"canonical_record":{"source":{"id":"1512.05434","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-12-17T01:27:51Z","cross_cats_sorted":["astro-ph.CO","hep-th","math-ph","math.MP"],"title_canon_sha256":"c389bc1a5db69d1522eb29ba3728fdd77ffd4ef9cba3d525f630c8bc71fad119","abstract_canon_sha256":"df05f33551b8db6b1d90bb7974fa9f86b65c373b85f8df91b637cc748a32eb75"},"schema_version":"1.0"},"canonical_sha256":"cec661736c7b696413af3bc297e9a1bdb43586ede6774cf0907a05a13c70475a","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:23:33.235020Z","signature_b64":"cAdh2RNHVwFuIrG1OMcFfiNisxFY2ROKLo2Ww5NhPWDxSmnuLOSoybIGGZ6Kow6y3yeH2NJPgJC6+OZAgqwGBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cec661736c7b696413af3bc297e9a1bdb43586ede6774cf0907a05a13c70475a","last_reissued_at":"2026-05-18T01:23:33.234173Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:23:33.234173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1512.05434","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":"2026-05-18T01:23:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"/zdy44TXXs8wrDfew0bGUCypZGYN6qm0qNcMMozurB5guvosBAr/dEjcbiLQ+Qxx5ed5CyFqRmSR9Ji4VOR8Bw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:20:48.000738Z"},"content_sha256":"2b8c4e2d394bf82dcd815a059d35901d57a276cf631a46c05b3663fb01090d82","schema_version":"1.0","event_id":"sha256:2b8c4e2d394bf82dcd815a059d35901d57a276cf631a46c05b3663fb01090d82"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2015:Z3DGC43MPNUWIE5PHPBJP2NBXW","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Closed-form solutions of the Wheeler-DeWitt equation in a scalar-vector field cosmological model by Lie symmetries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["astro-ph.CO","hep-th","math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"Andronikos Paliathanasis, Babak Vakili","submitted_at":"2015-12-17T01:27:51Z","abstract_excerpt":"We apply as selection rule to determine the unknown functions of a cosmological model the existence of Lie point symmetries for the Wheeler-DeWitt equation of quantum gravity. Our cosmological setting consists of a flat Friedmann-Robertson-Walker metric having the scale factor $a(t)$, a scalar field with potential function $V(\\phi)$ minimally coupled to gravity and a vector field of its kinetic energy is coupled with the scalar field by a coupling function $f(\\phi)$. Then, the Lie symmetries of this dynamical system are investigated by utilizing the behavior of the corresponding minisuperspace"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.05434","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":"2026-05-18T01:23:33Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"kAeL2lkK8iA75FANI9MXKPLyt27TupS3hf5WbWexGg+SyAImg9sZh1ZlLUwF49S9s80+5UZOMeWF1jlb7Mx1DQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-08T17:20:48.001417Z"},"content_sha256":"97ed5b0ed880e994cf2a46b299c448620eb2d0f1da6dafc868d41b07aa115135","schema_version":"1.0","event_id":"sha256:97ed5b0ed880e994cf2a46b299c448620eb2d0f1da6dafc868d41b07aa115135"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Z3DGC43MPNUWIE5PHPBJP2NBXW/bundle.json","state_url":"https://pith.science/pith/Z3DGC43MPNUWIE5PHPBJP2NBXW/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Z3DGC43MPNUWIE5PHPBJP2NBXW/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":"2026-06-08T17:20:48Z","links":{"resolver":"https://pith.science/pith/Z3DGC43MPNUWIE5PHPBJP2NBXW","bundle":"https://pith.science/pith/Z3DGC43MPNUWIE5PHPBJP2NBXW/bundle.json","state":"https://pith.science/pith/Z3DGC43MPNUWIE5PHPBJP2NBXW/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Z3DGC43MPNUWIE5PHPBJP2NBXW/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:Z3DGC43MPNUWIE5PHPBJP2NBXW","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":"df05f33551b8db6b1d90bb7974fa9f86b65c373b85f8df91b637cc748a32eb75","cross_cats_sorted":["astro-ph.CO","hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-12-17T01:27:51Z","title_canon_sha256":"c389bc1a5db69d1522eb29ba3728fdd77ffd4ef9cba3d525f630c8bc71fad119"},"schema_version":"1.0","source":{"id":"1512.05434","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1512.05434","created_at":"2026-05-18T01:23:33Z"},{"alias_kind":"arxiv_version","alias_value":"1512.05434v1","created_at":"2026-05-18T01:23:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.05434","created_at":"2026-05-18T01:23:33Z"},{"alias_kind":"pith_short_12","alias_value":"Z3DGC43MPNUW","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_16","alias_value":"Z3DGC43MPNUWIE5P","created_at":"2026-05-18T12:29:52Z"},{"alias_kind":"pith_short_8","alias_value":"Z3DGC43M","created_at":"2026-05-18T12:29:52Z"}],"graph_snapshots":[{"event_id":"sha256:97ed5b0ed880e994cf2a46b299c448620eb2d0f1da6dafc868d41b07aa115135","target":"graph","created_at":"2026-05-18T01:23:33Z","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":"We apply as selection rule to determine the unknown functions of a cosmological model the existence of Lie point symmetries for the Wheeler-DeWitt equation of quantum gravity. Our cosmological setting consists of a flat Friedmann-Robertson-Walker metric having the scale factor $a(t)$, a scalar field with potential function $V(\\phi)$ minimally coupled to gravity and a vector field of its kinetic energy is coupled with the scalar field by a coupling function $f(\\phi)$. Then, the Lie symmetries of this dynamical system are investigated by utilizing the behavior of the corresponding minisuperspace","authors_text":"Andronikos Paliathanasis, Babak Vakili","cross_cats":["astro-ph.CO","hep-th","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-12-17T01:27:51Z","title":"Closed-form solutions of the Wheeler-DeWitt equation in a scalar-vector field cosmological model by Lie symmetries"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.05434","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":"sha256:2b8c4e2d394bf82dcd815a059d35901d57a276cf631a46c05b3663fb01090d82","target":"record","created_at":"2026-05-18T01:23:33Z","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":"df05f33551b8db6b1d90bb7974fa9f86b65c373b85f8df91b637cc748a32eb75","cross_cats_sorted":["astro-ph.CO","hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2015-12-17T01:27:51Z","title_canon_sha256":"c389bc1a5db69d1522eb29ba3728fdd77ffd4ef9cba3d525f630c8bc71fad119"},"schema_version":"1.0","source":{"id":"1512.05434","kind":"arxiv","version":1}},"canonical_sha256":"cec661736c7b696413af3bc297e9a1bdb43586ede6774cf0907a05a13c70475a","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"cec661736c7b696413af3bc297e9a1bdb43586ede6774cf0907a05a13c70475a","first_computed_at":"2026-05-18T01:23:33.234173Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:23:33.234173Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cAdh2RNHVwFuIrG1OMcFfiNisxFY2ROKLo2Ww5NhPWDxSmnuLOSoybIGGZ6Kow6y3yeH2NJPgJC6+OZAgqwGBg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:23:33.235020Z","signed_message":"canonical_sha256_bytes"},"source_id":"1512.05434","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2b8c4e2d394bf82dcd815a059d35901d57a276cf631a46c05b3663fb01090d82","sha256:97ed5b0ed880e994cf2a46b299c448620eb2d0f1da6dafc868d41b07aa115135"],"state_sha256":"ddaf023519776e34ab903bb5296e84d08ad7d6b4873a2a6c8de4d3ccce21ed5a"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"I/dCOAgKEEeFXoZam4z3EVpNN5lc+DYmN3waCMrZs13uUFCSLO2A3OhrPuohqLTPAJgaR2e8ZmWNPlYDqyuJBA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-08T17:20:48.005595Z","bundle_sha256":"0ad26b5b97637ebb279943e31e3c405de1c01456eabbbaafcc22be34f31ce80a"}}