{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:Q2QBVVBMMD2INCHVHDRDJC2FRN","short_pith_number":"pith:Q2QBVVBM","canonical_record":{"source":{"id":"1807.06235","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-07-17T06:06:00Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"987c993c6c701cd2b3b423018fdb1db6bd152bc8d4a5690ae89bd2149c9cde86","abstract_canon_sha256":"b1c2447ee457679c6e6f3daec1f56c67836fb5c966e021a0588254cb195a7fbb"},"schema_version":"1.0"},"canonical_sha256":"86a01ad42c60f48688f538e2348b458b537e0bb19df876aa5ab99aed74264fd2","source":{"kind":"arxiv","id":"1807.06235","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.06235","created_at":"2026-07-05T00:28:21Z"},{"alias_kind":"arxiv_version","alias_value":"1807.06235v1","created_at":"2026-07-05T00:28:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.06235","created_at":"2026-07-05T00:28:21Z"},{"alias_kind":"pith_short_12","alias_value":"Q2QBVVBMMD2I","created_at":"2026-07-05T00:28:21Z"},{"alias_kind":"pith_short_16","alias_value":"Q2QBVVBMMD2INCHV","created_at":"2026-07-05T00:28:21Z"},{"alias_kind":"pith_short_8","alias_value":"Q2QBVVBM","created_at":"2026-07-05T00:28:21Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:Q2QBVVBMMD2INCHVHDRDJC2FRN","target":"record","payload":{"canonical_record":{"source":{"id":"1807.06235","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-07-17T06:06:00Z","cross_cats_sorted":["hep-th","math-ph","math.MP"],"title_canon_sha256":"987c993c6c701cd2b3b423018fdb1db6bd152bc8d4a5690ae89bd2149c9cde86","abstract_canon_sha256":"b1c2447ee457679c6e6f3daec1f56c67836fb5c966e021a0588254cb195a7fbb"},"schema_version":"1.0"},"canonical_sha256":"86a01ad42c60f48688f538e2348b458b537e0bb19df876aa5ab99aed74264fd2","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T00:28:21.739673Z","signature_b64":"0IxmYUdXvWOcRN/+EyP/0NM1m3797EelwFQDvAl6qn3kLoCxmHAspECwunkLzAc3wXbCFMOVMY/kteRaJTlJBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"86a01ad42c60f48688f538e2348b458b537e0bb19df876aa5ab99aed74264fd2","last_reissued_at":"2026-07-05T00:28:21.739198Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T00:28:21.739198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.06235","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":"2026-07-05T00:28:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZPDuJUs1pPPPvSuVtJ40eLQ9tfKvxgYT19NhZSpJcazDEj+ZuUhN5J6AZXHQSgDBmXWftAzgLnhFJysj/yuACg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T03:54:43.672147Z"},"content_sha256":"382fb074846d6359aedbe54543952a339ba2bf8c4828559369285eec90ee1257","schema_version":"1.0","event_id":"sha256:382fb074846d6359aedbe54543952a339ba2bf8c4828559369285eec90ee1257"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:Q2QBVVBMMD2INCHVHDRDJC2FRN","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Classical evolution of subspaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math-ph","math.MP"],"primary_cat":"gr-qc","authors_text":"Arkady A. Popov, Sergey G. Rubin, Yana Lyakhova","submitted_at":"2018-07-17T06:06:00Z","abstract_excerpt":"We study evolution of manifolds after their creation at high energies. Several kinds of gravitational Lagrangians with higher derivatives are considered. It is shown analytically and confirmed numerically that an asymptotic growth of the maximally symmetric manifolds depends strongly on their dimensionality. A number of final metrics describing our Universe is quite poor if we limit ourselves with a maximally symmetric extra space. We show that the initial conditions can be a reason of nontrivial solutions (funnels) and study their properties."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.06235","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1807.06235/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2026-07-05T00:28:21Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2llZtEtJiRuQwkU27FPPV3TjneUFyFn9vCfhxNaNGdcZFOWFYLWt6TvKvqC57fYCDW1ggLmBlvupqxZVKBGfCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-08-04T03:54:43.673031Z"},"content_sha256":"67c6f64d327fd98dd13da596fdf4b60760cf5b631e07760d0f8558da86d78149","schema_version":"1.0","event_id":"sha256:67c6f64d327fd98dd13da596fdf4b60760cf5b631e07760d0f8558da86d78149"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/Q2QBVVBMMD2INCHVHDRDJC2FRN/bundle.json","state_url":"https://pith.science/pith/Q2QBVVBMMD2INCHVHDRDJC2FRN/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/Q2QBVVBMMD2INCHVHDRDJC2FRN/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":"2026-08-04T03:54:43Z","links":{"resolver":"https://pith.science/pith/Q2QBVVBMMD2INCHVHDRDJC2FRN","bundle":"https://pith.science/pith/Q2QBVVBMMD2INCHVHDRDJC2FRN/bundle.json","state":"https://pith.science/pith/Q2QBVVBMMD2INCHVHDRDJC2FRN/state.json","well_known_bundle":"https://pith.science/.well-known/pith/Q2QBVVBMMD2INCHVHDRDJC2FRN/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:Q2QBVVBMMD2INCHVHDRDJC2FRN","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":"b1c2447ee457679c6e6f3daec1f56c67836fb5c966e021a0588254cb195a7fbb","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-07-17T06:06:00Z","title_canon_sha256":"987c993c6c701cd2b3b423018fdb1db6bd152bc8d4a5690ae89bd2149c9cde86"},"schema_version":"1.0","source":{"id":"1807.06235","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.06235","created_at":"2026-07-05T00:28:21Z"},{"alias_kind":"arxiv_version","alias_value":"1807.06235v1","created_at":"2026-07-05T00:28:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.06235","created_at":"2026-07-05T00:28:21Z"},{"alias_kind":"pith_short_12","alias_value":"Q2QBVVBMMD2I","created_at":"2026-07-05T00:28:21Z"},{"alias_kind":"pith_short_16","alias_value":"Q2QBVVBMMD2INCHV","created_at":"2026-07-05T00:28:21Z"},{"alias_kind":"pith_short_8","alias_value":"Q2QBVVBM","created_at":"2026-07-05T00:28:21Z"}],"graph_snapshots":[{"event_id":"sha256:67c6f64d327fd98dd13da596fdf4b60760cf5b631e07760d0f8558da86d78149","target":"graph","created_at":"2026-07-05T00:28:21Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/1807.06235/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study evolution of manifolds after their creation at high energies. Several kinds of gravitational Lagrangians with higher derivatives are considered. It is shown analytically and confirmed numerically that an asymptotic growth of the maximally symmetric manifolds depends strongly on their dimensionality. A number of final metrics describing our Universe is quite poor if we limit ourselves with a maximally symmetric extra space. We show that the initial conditions can be a reason of nontrivial solutions (funnels) and study their properties.","authors_text":"Arkady A. Popov, Sergey G. Rubin, Yana Lyakhova","cross_cats":["hep-th","math-ph","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-07-17T06:06:00Z","title":"Classical evolution of subspaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.06235","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":"sha256:382fb074846d6359aedbe54543952a339ba2bf8c4828559369285eec90ee1257","target":"record","created_at":"2026-07-05T00:28:21Z","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":"b1c2447ee457679c6e6f3daec1f56c67836fb5c966e021a0588254cb195a7fbb","cross_cats_sorted":["hep-th","math-ph","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"gr-qc","submitted_at":"2018-07-17T06:06:00Z","title_canon_sha256":"987c993c6c701cd2b3b423018fdb1db6bd152bc8d4a5690ae89bd2149c9cde86"},"schema_version":"1.0","source":{"id":"1807.06235","kind":"arxiv","version":1}},"canonical_sha256":"86a01ad42c60f48688f538e2348b458b537e0bb19df876aa5ab99aed74264fd2","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"86a01ad42c60f48688f538e2348b458b537e0bb19df876aa5ab99aed74264fd2","first_computed_at":"2026-07-05T00:28:21.739198Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T00:28:21.739198Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"0IxmYUdXvWOcRN/+EyP/0NM1m3797EelwFQDvAl6qn3kLoCxmHAspECwunkLzAc3wXbCFMOVMY/kteRaJTlJBA==","signature_status":"signed_v1","signed_at":"2026-07-05T00:28:21.739673Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.06235","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:382fb074846d6359aedbe54543952a339ba2bf8c4828559369285eec90ee1257","sha256:67c6f64d327fd98dd13da596fdf4b60760cf5b631e07760d0f8558da86d78149"],"state_sha256":"fa2e47d0b54f70c7e982f82ac4f7ec5ba138e50a7ad0da1408037136c6cde828"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"lZlaoOyhWMyF+DT/IjVzWGJ2uSH910NO4j+doFRC0OntZrgS1uYhd75ATDiDDxRhP/voyrIrnqyzx/BhP1zGCg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-08-04T03:54:43.678121Z","bundle_sha256":"a87975ea0f8ce35cc712504878dfd999c339810d6931ca222d3043c94963a30f"}}