{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2014:3X5AABQFAUUAVWLF3RCDQKOBYG","short_pith_number":"pith:3X5AABQF","canonical_record":{"source":{"id":"1405.4231","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-05-16T16:30:08Z","cross_cats_sorted":[],"title_canon_sha256":"88c29d9c4e6a93a78ec5d46b3f3ded827f838a1d9eb0595ee4c05bef9fb56ba2","abstract_canon_sha256":"3b1a859c9d12c69f1c1445d1604d627985a90dbdd8ecf8af05a28ece213a685d"},"schema_version":"1.0"},"canonical_sha256":"ddfa00060505280ad965dc443829c1c18a300a5cc3a5ff0e9fadd6dcd9b01705","source":{"kind":"arxiv","id":"1405.4231","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.4231","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"arxiv_version","alias_value":"1405.4231v1","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.4231","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"pith_short_12","alias_value":"3X5AABQFAUUA","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3X5AABQFAUUAVWLF","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3X5AABQF","created_at":"2026-05-18T12:28:11Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2014:3X5AABQFAUUAVWLF3RCDQKOBYG","target":"record","payload":{"canonical_record":{"source":{"id":"1405.4231","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-05-16T16:30:08Z","cross_cats_sorted":[],"title_canon_sha256":"88c29d9c4e6a93a78ec5d46b3f3ded827f838a1d9eb0595ee4c05bef9fb56ba2","abstract_canon_sha256":"3b1a859c9d12c69f1c1445d1604d627985a90dbdd8ecf8af05a28ece213a685d"},"schema_version":"1.0"},"canonical_sha256":"ddfa00060505280ad965dc443829c1c18a300a5cc3a5ff0e9fadd6dcd9b01705","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:42.883218Z","signature_b64":"nUIfKkEkl5xfvcC3HcZFsC7+EVjgYElvA5KcYIKPeLU9NhO/S5c3RsRVcgE2vKuNRwZNrvhjUjFJPtFg4zApDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ddfa00060505280ad965dc443829c1c18a300a5cc3a5ff0e9fadd6dcd9b01705","last_reissued_at":"2026-05-18T02:51:42.882741Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:42.882741Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1405.4231","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":"2026-05-18T02:51:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"F/C4M2mg7BGjgWocwA73nDw1j09PyrzVO+dQ8Uo6mXFZrSjT/z5UtyH7PdKUc/azVNv9JZHsq2H48yDUqz66BA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T18:55:35.448301Z"},"content_sha256":"06539b737d95bad5a377643d6bfd6f44d85899a93fb59b2e57dd1332cb670846","schema_version":"1.0","event_id":"sha256:06539b737d95bad5a377643d6bfd6f44d85899a93fb59b2e57dd1332cb670846"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2014:3X5AABQFAUUAVWLF3RCDQKOBYG","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The Geometry of Loop Spaces I: $H^s$-Riemannian Metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DG","authors_text":"Fabi\\'an Torres-Ardila, Steven Rosenberg, Yoshiaki Maeda","submitted_at":"2014-05-16T16:30:08Z","abstract_excerpt":"A Riemannian metric on a manifold M induces a family of Riemannian metrics on the loop space LM depending on a Sobolev space parameter s. We compute the connection forms of these metrics and the higher symbols of their curvature forms, which take values in pseudodifferential operators. These calculations are used in a followup paper \"The Geometry of Loop Spaces II: Characteristic Classes\" to construct Chern-Simons classes on the tangent bundle TLM which detect nontrivial elements in the diffeomorphism group of certain Sasakian 5-manifolds associated to Kaehler surfaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4231","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":"2026-05-18T02:51:42Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"9WoK7mVmows8cyFV0R/itq+oPP5RV5hq2potpko0h8kYQn7HJMDaxvAvCIHREL/ppzoxxOgcbOjyJ7kICkUDCQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T18:55:35.448677Z"},"content_sha256":"dc44e962f044f73a72b282f58ff63d3d0edc0ec8456b974ff24e8b69f5bf3ded","schema_version":"1.0","event_id":"sha256:dc44e962f044f73a72b282f58ff63d3d0edc0ec8456b974ff24e8b69f5bf3ded"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3X5AABQFAUUAVWLF3RCDQKOBYG/bundle.json","state_url":"https://pith.science/pith/3X5AABQFAUUAVWLF3RCDQKOBYG/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3X5AABQFAUUAVWLF3RCDQKOBYG/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":"2026-06-25T18:55:35Z","links":{"resolver":"https://pith.science/pith/3X5AABQFAUUAVWLF3RCDQKOBYG","bundle":"https://pith.science/pith/3X5AABQFAUUAVWLF3RCDQKOBYG/bundle.json","state":"https://pith.science/pith/3X5AABQFAUUAVWLF3RCDQKOBYG/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3X5AABQFAUUAVWLF3RCDQKOBYG/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:3X5AABQFAUUAVWLF3RCDQKOBYG","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":"3b1a859c9d12c69f1c1445d1604d627985a90dbdd8ecf8af05a28ece213a685d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-05-16T16:30:08Z","title_canon_sha256":"88c29d9c4e6a93a78ec5d46b3f3ded827f838a1d9eb0595ee4c05bef9fb56ba2"},"schema_version":"1.0","source":{"id":"1405.4231","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1405.4231","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"arxiv_version","alias_value":"1405.4231v1","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.4231","created_at":"2026-05-18T02:51:42Z"},{"alias_kind":"pith_short_12","alias_value":"3X5AABQFAUUA","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_16","alias_value":"3X5AABQFAUUAVWLF","created_at":"2026-05-18T12:28:11Z"},{"alias_kind":"pith_short_8","alias_value":"3X5AABQF","created_at":"2026-05-18T12:28:11Z"}],"graph_snapshots":[{"event_id":"sha256:dc44e962f044f73a72b282f58ff63d3d0edc0ec8456b974ff24e8b69f5bf3ded","target":"graph","created_at":"2026-05-18T02:51:42Z","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":"A Riemannian metric on a manifold M induces a family of Riemannian metrics on the loop space LM depending on a Sobolev space parameter s. We compute the connection forms of these metrics and the higher symbols of their curvature forms, which take values in pseudodifferential operators. These calculations are used in a followup paper \"The Geometry of Loop Spaces II: Characteristic Classes\" to construct Chern-Simons classes on the tangent bundle TLM which detect nontrivial elements in the diffeomorphism group of certain Sasakian 5-manifolds associated to Kaehler surfaces.","authors_text":"Fabi\\'an Torres-Ardila, Steven Rosenberg, Yoshiaki Maeda","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-05-16T16:30:08Z","title":"The Geometry of Loop Spaces I: $H^s$-Riemannian Metrics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.4231","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":"sha256:06539b737d95bad5a377643d6bfd6f44d85899a93fb59b2e57dd1332cb670846","target":"record","created_at":"2026-05-18T02:51:42Z","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":"3b1a859c9d12c69f1c1445d1604d627985a90dbdd8ecf8af05a28ece213a685d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-05-16T16:30:08Z","title_canon_sha256":"88c29d9c4e6a93a78ec5d46b3f3ded827f838a1d9eb0595ee4c05bef9fb56ba2"},"schema_version":"1.0","source":{"id":"1405.4231","kind":"arxiv","version":1}},"canonical_sha256":"ddfa00060505280ad965dc443829c1c18a300a5cc3a5ff0e9fadd6dcd9b01705","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"ddfa00060505280ad965dc443829c1c18a300a5cc3a5ff0e9fadd6dcd9b01705","first_computed_at":"2026-05-18T02:51:42.882741Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:51:42.882741Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"nUIfKkEkl5xfvcC3HcZFsC7+EVjgYElvA5KcYIKPeLU9NhO/S5c3RsRVcgE2vKuNRwZNrvhjUjFJPtFg4zApDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:51:42.883218Z","signed_message":"canonical_sha256_bytes"},"source_id":"1405.4231","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:06539b737d95bad5a377643d6bfd6f44d85899a93fb59b2e57dd1332cb670846","sha256:dc44e962f044f73a72b282f58ff63d3d0edc0ec8456b974ff24e8b69f5bf3ded"],"state_sha256":"a1245b7e0213e5fc2007983788d2dc0fb711bb74340f937ec160318441bf5b69"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"0fd9LQL+fIcdh1iyzYRUSOfMQTBtej3D9bs5Qc5XCq1g7g3C9FPsTHw3wSPrdMJYeU438AC8jHkANlAk0LPODQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T18:55:35.450626Z","bundle_sha256":"b9453f560569660718e426264d96a99a9468643fdab949e930d91371eb9bfb1f"}}