{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2006:P63HV2YTW4FMYVR4F52GKWAEL2","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":"7958f4e9f26f6183f78b473f44deb35310677fd886870eb1064d58d4f1ea93e0","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"2006-10-26T15:52:51Z","title_canon_sha256":"f31655d3af1102125e0a1280f443b9baf30e2196468573cc529a94c200b18f4a"},"schema_version":"1.0","source":{"id":"hep-th/0610281","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"hep-th/0610281","created_at":"2026-05-18T04:38:26Z"},{"alias_kind":"arxiv_version","alias_value":"hep-th/0610281v3","created_at":"2026-05-18T04:38:26Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.hep-th/0610281","created_at":"2026-05-18T04:38:26Z"},{"alias_kind":"pith_short_12","alias_value":"P63HV2YTW4FM","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_16","alias_value":"P63HV2YTW4FMYVR4","created_at":"2026-05-18T12:25:54Z"},{"alias_kind":"pith_short_8","alias_value":"P63HV2YT","created_at":"2026-05-18T12:25:54Z"}],"graph_snapshots":[{"event_id":"sha256:45f1b7171160461c2429f280659ae19e28e3c34bc7f776ac55f952651c7c125f","target":"graph","created_at":"2026-05-18T04:38:26Z","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 study renormalization-group flows by deforming a class of conformal sigma-models. We consider overall scale factor perturbation of Einstein spaces as well as more general anisotropic deformations of three-spheres. At leading order in alpha, renormalization-group equations turn out to be Ricci flows. In the three-sphere background, the latter is the Halphen system, which is exactly solvable in terms of modular forms. We also analyze time-dependent deformations of these systems supplemented with an extra time coordinate and time-dependent dilaton. In some regimes time evolution is identified ","authors_text":"Domenico Orlando, Ioannis Bakas, P. Marios Petropoulos","cross_cats":[],"headline":"","license":"","primary_cat":"hep-th","submitted_at":"2006-10-26T15:52:51Z","title":"Ricci flows and expansion in axion-dilaton cosmology"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"hep-th/0610281","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:e7ed3114be42b0b6faf9fe315cfcb2e638f0ee0da7ac01c7fce42540965b40f2","target":"record","created_at":"2026-05-18T04:38:26Z","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":"7958f4e9f26f6183f78b473f44deb35310677fd886870eb1064d58d4f1ea93e0","cross_cats_sorted":[],"license":"","primary_cat":"hep-th","submitted_at":"2006-10-26T15:52:51Z","title_canon_sha256":"f31655d3af1102125e0a1280f443b9baf30e2196468573cc529a94c200b18f4a"},"schema_version":"1.0","source":{"id":"hep-th/0610281","kind":"arxiv","version":3}},"canonical_sha256":"7fb67aeb13b70acc563c2f746558045eb4633a61bfa9c473bac49fdf3a073ff5","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7fb67aeb13b70acc563c2f746558045eb4633a61bfa9c473bac49fdf3a073ff5","first_computed_at":"2026-05-18T04:38:26.204181Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:38:26.204181Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"n0Rwj+SWqcdke59FPz5ojs2ZWzX5nNovJQXhnxX3S13FbM82rZeB0QD2wZDAxGNWBds9AIPgCLRFJ8ZHGuX8AA==","signature_status":"signed_v1","signed_at":"2026-05-18T04:38:26.204883Z","signed_message":"canonical_sha256_bytes"},"source_id":"hep-th/0610281","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:e7ed3114be42b0b6faf9fe315cfcb2e638f0ee0da7ac01c7fce42540965b40f2","sha256:45f1b7171160461c2429f280659ae19e28e3c34bc7f776ac55f952651c7c125f"],"state_sha256":"62df0711d492b138e276f57fee3b3b93ba8ae4bf8c1898f21212d41898923163"}