{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2010:HGHHX5MAA4NPPLA533J3JDLHPZ","short_pith_number":"pith:HGHHX5MA","canonical_record":{"source":{"id":"1011.1106","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-11-04T10:42:26Z","cross_cats_sorted":[],"title_canon_sha256":"58c91bc30fc5448a10ffd46c355f4a22b72cf3be12d2eace8b2638860847bce6","abstract_canon_sha256":"95ba1e86b126b93b60c1bd3cd0a0ccab4a1f7624c093c2eb259a40dcceedb990"},"schema_version":"1.0"},"canonical_sha256":"398e7bf580071af7ac1dded3b48d677e7867982e221be20e2152b351f53a6867","source":{"kind":"arxiv","id":"1011.1106","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.1106","created_at":"2026-05-18T04:37:01Z"},{"alias_kind":"arxiv_version","alias_value":"1011.1106v1","created_at":"2026-05-18T04:37:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.1106","created_at":"2026-05-18T04:37:01Z"},{"alias_kind":"pith_short_12","alias_value":"HGHHX5MAA4NP","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"HGHHX5MAA4NPPLA5","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"HGHHX5MA","created_at":"2026-05-18T12:26:07Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2010:HGHHX5MAA4NPPLA533J3JDLHPZ","target":"record","payload":{"canonical_record":{"source":{"id":"1011.1106","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-11-04T10:42:26Z","cross_cats_sorted":[],"title_canon_sha256":"58c91bc30fc5448a10ffd46c355f4a22b72cf3be12d2eace8b2638860847bce6","abstract_canon_sha256":"95ba1e86b126b93b60c1bd3cd0a0ccab4a1f7624c093c2eb259a40dcceedb990"},"schema_version":"1.0"},"canonical_sha256":"398e7bf580071af7ac1dded3b48d677e7867982e221be20e2152b351f53a6867","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:37:01.987999Z","signature_b64":"Wx8nchoJSw0mZPIBUX9mVHutJtyjkZXWhWSXSt8ycg5pA84OQR2aiwB0LHHkNvNR/67Gs91HqDfA80bNvECmBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"398e7bf580071af7ac1dded3b48d677e7867982e221be20e2152b351f53a6867","last_reissued_at":"2026-05-18T04:37:01.987498Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:37:01.987498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1011.1106","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":"2026-05-18T04:37:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"NDavWNSISyKZwSZhV0jw5K0niuuGUABNaPt1DVvm5RJkM2GTf9Mp9ktWgODyCByBicbzb2syHzqfVQVyLnqSDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T00:50:47.474966Z"},"content_sha256":"1f82c222a998d1bcd17cea1b878c738ccd30af9c764255c696dc0075f09f79ab","schema_version":"1.0","event_id":"sha256:1f82c222a998d1bcd17cea1b878c738ccd30af9c764255c696dc0075f09f79ab"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2010:HGHHX5MAA4NPPLA533J3JDLHPZ","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Geometric flows and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"hep-th","authors_text":"Marios Petropoulos","submitted_at":"2010-11-04T10:42:26Z","abstract_excerpt":"I present some applications of geometric flows in string theory and gravity. In some circumstances time evolution in string theory can be approximately identified with Ricci-flow parametric evolution of spatial sections. In four dimensions, homogeneous, self-dual, gravitational instantons of general relativity evolve in time exactly as geometric flows of homogeneous three-manifolds. For non-relativistic versions of gravity, this property persists in any dimension, under the assumption of detailed-balance condition."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1106","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":"2026-05-18T04:37:01Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"t9n9IFJ1L9GDi/TRQXq4sqE//tm01O2zt+jaxtRa9Fk/uIoTGPJRDo6zi3bMtLYlfw8fuY+SV5B7jhQ9dPQyCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-11T00:50:47.475656Z"},"content_sha256":"43a7b85345c9d53988d4b7c3c09cf4503ab22f2a0b13f8bb1547a8e988c4377b","schema_version":"1.0","event_id":"sha256:43a7b85345c9d53988d4b7c3c09cf4503ab22f2a0b13f8bb1547a8e988c4377b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/HGHHX5MAA4NPPLA533J3JDLHPZ/bundle.json","state_url":"https://pith.science/pith/HGHHX5MAA4NPPLA533J3JDLHPZ/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/HGHHX5MAA4NPPLA533J3JDLHPZ/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":"2026-06-11T00:50:47Z","links":{"resolver":"https://pith.science/pith/HGHHX5MAA4NPPLA533J3JDLHPZ","bundle":"https://pith.science/pith/HGHHX5MAA4NPPLA533J3JDLHPZ/bundle.json","state":"https://pith.science/pith/HGHHX5MAA4NPPLA533J3JDLHPZ/state.json","well_known_bundle":"https://pith.science/.well-known/pith/HGHHX5MAA4NPPLA533J3JDLHPZ/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:HGHHX5MAA4NPPLA533J3JDLHPZ","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":"95ba1e86b126b93b60c1bd3cd0a0ccab4a1f7624c093c2eb259a40dcceedb990","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-11-04T10:42:26Z","title_canon_sha256":"58c91bc30fc5448a10ffd46c355f4a22b72cf3be12d2eace8b2638860847bce6"},"schema_version":"1.0","source":{"id":"1011.1106","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1011.1106","created_at":"2026-05-18T04:37:01Z"},{"alias_kind":"arxiv_version","alias_value":"1011.1106v1","created_at":"2026-05-18T04:37:01Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1011.1106","created_at":"2026-05-18T04:37:01Z"},{"alias_kind":"pith_short_12","alias_value":"HGHHX5MAA4NP","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_16","alias_value":"HGHHX5MAA4NPPLA5","created_at":"2026-05-18T12:26:07Z"},{"alias_kind":"pith_short_8","alias_value":"HGHHX5MA","created_at":"2026-05-18T12:26:07Z"}],"graph_snapshots":[{"event_id":"sha256:43a7b85345c9d53988d4b7c3c09cf4503ab22f2a0b13f8bb1547a8e988c4377b","target":"graph","created_at":"2026-05-18T04:37:01Z","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":"I present some applications of geometric flows in string theory and gravity. In some circumstances time evolution in string theory can be approximately identified with Ricci-flow parametric evolution of spatial sections. In four dimensions, homogeneous, self-dual, gravitational instantons of general relativity evolve in time exactly as geometric flows of homogeneous three-manifolds. For non-relativistic versions of gravity, this property persists in any dimension, under the assumption of detailed-balance condition.","authors_text":"Marios Petropoulos","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-11-04T10:42:26Z","title":"Geometric flows and applications"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.1106","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":"sha256:1f82c222a998d1bcd17cea1b878c738ccd30af9c764255c696dc0075f09f79ab","target":"record","created_at":"2026-05-18T04:37:01Z","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":"95ba1e86b126b93b60c1bd3cd0a0ccab4a1f7624c093c2eb259a40dcceedb990","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"hep-th","submitted_at":"2010-11-04T10:42:26Z","title_canon_sha256":"58c91bc30fc5448a10ffd46c355f4a22b72cf3be12d2eace8b2638860847bce6"},"schema_version":"1.0","source":{"id":"1011.1106","kind":"arxiv","version":1}},"canonical_sha256":"398e7bf580071af7ac1dded3b48d677e7867982e221be20e2152b351f53a6867","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"398e7bf580071af7ac1dded3b48d677e7867982e221be20e2152b351f53a6867","first_computed_at":"2026-05-18T04:37:01.987498Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:37:01.987498Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"Wx8nchoJSw0mZPIBUX9mVHutJtyjkZXWhWSXSt8ycg5pA84OQR2aiwB0LHHkNvNR/67Gs91HqDfA80bNvECmBg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:37:01.987999Z","signed_message":"canonical_sha256_bytes"},"source_id":"1011.1106","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1f82c222a998d1bcd17cea1b878c738ccd30af9c764255c696dc0075f09f79ab","sha256:43a7b85345c9d53988d4b7c3c09cf4503ab22f2a0b13f8bb1547a8e988c4377b"],"state_sha256":"671e3c1780758d38c6d6388f12132bbb3795ec3a90e4058734ac8be01e7ed0e2"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"VOASpQC0fv317ydgHgTtVsfRIkTLxczWZDRnCr8t6VLgRo1IwRrL/ZtuGh5xWzJWW4YSUV/FIQFTxg6StocfAg==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-11T00:50:47.480271Z","bundle_sha256":"62bc4e421cb1385ebca946eb8fa035c1d98b33dcbed27d0b4bff9a7dbc1ef017"}}