{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2022:WYF537VE3FM46IW2TSHUGSALIX","short_pith_number":"pith:WYF537VE","canonical_record":{"source":{"id":"2206.09198","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-06-18T12:44:57Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"fe077b3645d04490292c94f5a90ab443e2b1d3d61577ed5d1be9b1d11607a666","abstract_canon_sha256":"68eca652c3f5ccf67ed4facf8720041e0399f65b402e62820f5492f89d6b8b1a"},"schema_version":"1.0"},"canonical_sha256":"b60bddfea4d959cf22da9c8f43480b45c861a270684d542a6f8ef04ff8d7266b","source":{"kind":"arxiv","id":"2206.09198","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.09198","created_at":"2026-07-05T04:33:05Z"},{"alias_kind":"arxiv_version","alias_value":"2206.09198v1","created_at":"2026-07-05T04:33:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.09198","created_at":"2026-07-05T04:33:05Z"},{"alias_kind":"pith_short_12","alias_value":"WYF537VE3FM4","created_at":"2026-07-05T04:33:05Z"},{"alias_kind":"pith_short_16","alias_value":"WYF537VE3FM46IW2","created_at":"2026-07-05T04:33:05Z"},{"alias_kind":"pith_short_8","alias_value":"WYF537VE","created_at":"2026-07-05T04:33:05Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2022:WYF537VE3FM46IW2TSHUGSALIX","target":"record","payload":{"canonical_record":{"source":{"id":"2206.09198","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-06-18T12:44:57Z","cross_cats_sorted":["math-ph","math.AP","math.MP"],"title_canon_sha256":"fe077b3645d04490292c94f5a90ab443e2b1d3d61577ed5d1be9b1d11607a666","abstract_canon_sha256":"68eca652c3f5ccf67ed4facf8720041e0399f65b402e62820f5492f89d6b8b1a"},"schema_version":"1.0"},"canonical_sha256":"b60bddfea4d959cf22da9c8f43480b45c861a270684d542a6f8ef04ff8d7266b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T04:33:05.033896Z","signature_b64":"1txkm7XHTP5tksA2ijllP6npyT7FixE7h64+4iz1mIOM6jcKA5hsctuja2n9jei9WSW0bnXb8v8P3aPwOkQIBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b60bddfea4d959cf22da9c8f43480b45c861a270684d542a6f8ef04ff8d7266b","last_reissued_at":"2026-07-05T04:33:05.033524Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T04:33:05.033524Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"2206.09198","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":"2026-07-05T04:33:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"spirVKvZczR0MWR4H8pGl2f0vdLpbejLoJn+JVZ5+Ihk9R2LOtPz+6Bk7fphCAsyDHfcjGqUD5exv0QYZAP/AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-26T12:39:23.751099Z"},"content_sha256":"b969d1f7621b86bf74c16aa5bc8089bcf167bb662d4c308fafcaa50b13da4044","schema_version":"1.0","event_id":"sha256:b969d1f7621b86bf74c16aa5bc8089bcf167bb662d4c308fafcaa50b13da4044"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2022:WYF537VE3FM46IW2TSHUGSALIX","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The spinorial energy for asymptotically Euclidean Ricci flow","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.AP","math.MP"],"primary_cat":"math.DG","authors_text":"Julius Baldauf, Tristan Ozuch","submitted_at":"2022-06-18T12:44:57Z","abstract_excerpt":"This paper introduces a functional generalizing Perelman's weighted Hilbert-Einstein action and the Dirichlet energy for spinors. It is well-defined on a wide class of non-compact manifolds; on asymptotically Euclidean manifolds, the functional is shown to admit a unique critical point, which is necessarily of min-max type, and Ricci flow is its gradient flow. The proof is based on variational formulas for weighted spinorial functionals, valid on all spin manifolds with boundary."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.09198","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/2206.09198/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":"2026-07-05T04:33:05Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ZkNc59ba5XQtUNIujZR6tXZ9esFMdWQAtAYD4H3bEXoOb5g6vbzruEGHPtj7xOq4ngyE3pm8dbxuHN4+wYeiAA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-26T12:39:23.751497Z"},"content_sha256":"7911d461d1a1666d9cbc771483b37c996ae85c90c984b1d1e26e0e5e734791c5","schema_version":"1.0","event_id":"sha256:7911d461d1a1666d9cbc771483b37c996ae85c90c984b1d1e26e0e5e734791c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WYF537VE3FM46IW2TSHUGSALIX/bundle.json","state_url":"https://pith.science/pith/WYF537VE3FM46IW2TSHUGSALIX/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WYF537VE3FM46IW2TSHUGSALIX/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":"2026-07-26T12:39:23Z","links":{"resolver":"https://pith.science/pith/WYF537VE3FM46IW2TSHUGSALIX","bundle":"https://pith.science/pith/WYF537VE3FM46IW2TSHUGSALIX/bundle.json","state":"https://pith.science/pith/WYF537VE3FM46IW2TSHUGSALIX/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WYF537VE3FM46IW2TSHUGSALIX/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2022:WYF537VE3FM46IW2TSHUGSALIX","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":"68eca652c3f5ccf67ed4facf8720041e0399f65b402e62820f5492f89d6b8b1a","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-06-18T12:44:57Z","title_canon_sha256":"fe077b3645d04490292c94f5a90ab443e2b1d3d61577ed5d1be9b1d11607a666"},"schema_version":"1.0","source":{"id":"2206.09198","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2206.09198","created_at":"2026-07-05T04:33:05Z"},{"alias_kind":"arxiv_version","alias_value":"2206.09198v1","created_at":"2026-07-05T04:33:05Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2206.09198","created_at":"2026-07-05T04:33:05Z"},{"alias_kind":"pith_short_12","alias_value":"WYF537VE3FM4","created_at":"2026-07-05T04:33:05Z"},{"alias_kind":"pith_short_16","alias_value":"WYF537VE3FM46IW2","created_at":"2026-07-05T04:33:05Z"},{"alias_kind":"pith_short_8","alias_value":"WYF537VE","created_at":"2026-07-05T04:33:05Z"}],"graph_snapshots":[{"event_id":"sha256:7911d461d1a1666d9cbc771483b37c996ae85c90c984b1d1e26e0e5e734791c5","target":"graph","created_at":"2026-07-05T04:33:05Z","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/2206.09198/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"This paper introduces a functional generalizing Perelman's weighted Hilbert-Einstein action and the Dirichlet energy for spinors. It is well-defined on a wide class of non-compact manifolds; on asymptotically Euclidean manifolds, the functional is shown to admit a unique critical point, which is necessarily of min-max type, and Ricci flow is its gradient flow. The proof is based on variational formulas for weighted spinorial functionals, valid on all spin manifolds with boundary.","authors_text":"Julius Baldauf, Tristan Ozuch","cross_cats":["math-ph","math.AP","math.MP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-06-18T12:44:57Z","title":"The spinorial energy for asymptotically Euclidean Ricci flow"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2206.09198","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:b969d1f7621b86bf74c16aa5bc8089bcf167bb662d4c308fafcaa50b13da4044","target":"record","created_at":"2026-07-05T04:33:05Z","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":"68eca652c3f5ccf67ed4facf8720041e0399f65b402e62820f5492f89d6b8b1a","cross_cats_sorted":["math-ph","math.AP","math.MP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2022-06-18T12:44:57Z","title_canon_sha256":"fe077b3645d04490292c94f5a90ab443e2b1d3d61577ed5d1be9b1d11607a666"},"schema_version":"1.0","source":{"id":"2206.09198","kind":"arxiv","version":1}},"canonical_sha256":"b60bddfea4d959cf22da9c8f43480b45c861a270684d542a6f8ef04ff8d7266b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b60bddfea4d959cf22da9c8f43480b45c861a270684d542a6f8ef04ff8d7266b","first_computed_at":"2026-07-05T04:33:05.033524Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T04:33:05.033524Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1txkm7XHTP5tksA2ijllP6npyT7FixE7h64+4iz1mIOM6jcKA5hsctuja2n9jei9WSW0bnXb8v8P3aPwOkQIBA==","signature_status":"signed_v1","signed_at":"2026-07-05T04:33:05.033896Z","signed_message":"canonical_sha256_bytes"},"source_id":"2206.09198","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b969d1f7621b86bf74c16aa5bc8089bcf167bb662d4c308fafcaa50b13da4044","sha256:7911d461d1a1666d9cbc771483b37c996ae85c90c984b1d1e26e0e5e734791c5"],"state_sha256":"0929e364f41937ebf5afc530288248883c447d5f932aa2a170f23d68ff596ab1"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"1Ed0H9HuETit09UebedsTodJnAz+jydqQzfaA3pYK37apnwn9ebRAcxxWQyvY3ODsp+YJ7/hdwJz5ySVXDU/AQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-26T12:39:23.753955Z","bundle_sha256":"d1e48a485dcee061a0f0eafe4f11a52aacc8d66a0588355da854a41a11a1e7a8"}}