{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:6UPZHYLIQVVI4V3MNEVEEQ6K3R","short_pith_number":"pith:6UPZHYLI","canonical_record":{"source":{"id":"1310.1136","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-10-03T23:54:41Z","cross_cats_sorted":["math.DG","math.GR","math.KT"],"title_canon_sha256":"237a9f92381973a0a27c96f027826d5b97e7687fc7c5fbcfc5b3ecc744e68708","abstract_canon_sha256":"00fc97d49b387fa6356386c86f9cf88e2553674bdf80fe9d1deca4870ba27994"},"schema_version":"1.0"},"canonical_sha256":"f51f93e168856a8e576c692a4243cadc7d39a8ece5e504dd0e3fe4a4235dc723","source":{"kind":"arxiv","id":"1310.1136","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.1136","created_at":"2026-05-18T02:44:31Z"},{"alias_kind":"arxiv_version","alias_value":"1310.1136v2","created_at":"2026-05-18T02:44:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.1136","created_at":"2026-05-18T02:44:31Z"},{"alias_kind":"pith_short_12","alias_value":"6UPZHYLIQVVI","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6UPZHYLIQVVI4V3M","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6UPZHYLI","created_at":"2026-05-18T12:27:36Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:6UPZHYLIQVVI4V3MNEVEEQ6K3R","target":"record","payload":{"canonical_record":{"source":{"id":"1310.1136","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-10-03T23:54:41Z","cross_cats_sorted":["math.DG","math.GR","math.KT"],"title_canon_sha256":"237a9f92381973a0a27c96f027826d5b97e7687fc7c5fbcfc5b3ecc744e68708","abstract_canon_sha256":"00fc97d49b387fa6356386c86f9cf88e2553674bdf80fe9d1deca4870ba27994"},"schema_version":"1.0"},"canonical_sha256":"f51f93e168856a8e576c692a4243cadc7d39a8ece5e504dd0e3fe4a4235dc723","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:44:31.889116Z","signature_b64":"iL7pqGswgDES3ezMn9k3gVbZe7ekx844blmavZqgfzVrv1niAm3LSyGhm1T83g3KbgXwcfE1DXtw/OrVRgRlCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f51f93e168856a8e576c692a4243cadc7d39a8ece5e504dd0e3fe4a4235dc723","last_reissued_at":"2026-05-18T02:44:31.888551Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:44:31.888551Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1310.1136","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:44:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"52GWZs+FPjsjAPAj+tLFQxu3sDo3SW1tJH0S31V4+8BwnFoU+aoyrcmJmA4pDh+FIr9Dmos2K1UUH39H4dpnCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T12:25:27.497707Z"},"content_sha256":"110ecedbe9950b8d4de7e600df483ee91ecb5f79c176e0ebe904e987ece2dbea","schema_version":"1.0","event_id":"sha256:110ecedbe9950b8d4de7e600df483ee91ecb5f79c176e0ebe904e987ece2dbea"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:6UPZHYLIQVVI4V3MNEVEEQ6K3R","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Higher rho invariants and the moduli space of positive scalar curvature metrics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG","math.GR","math.KT"],"primary_cat":"math.OA","authors_text":"Guoliang Yu, Zhizhang Xie","submitted_at":"2013-10-03T23:54:41Z","abstract_excerpt":"Given a closed smooth manifold M which carries a positive scalar curvature metric, one can associate an abelian group P(M) to the space of positive scalar curvature metrics on this manifold. The group of all diffeomorphisms of the manifold naturally acts on P(M). The moduli group of positive scalar curvature metrics is defined to be the quotient abelian group of this action, i.e. the coinvariant of the action. The moduli group measures the size of the moduli space of positive scalar curvature metrics on M. In this paper, we use the higher rho invariant and the finite part of the K-theory of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1136","kind":"arxiv","version":2},"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":"2026-05-18T02:44:31Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"WqGLUuDvtgeL+hJ/3dHElMnvw1QKLF3t9lEFu5FAwkUZc0Q+/r1vzFHD+05T62cLQ+v6OGcoRqnX4ZZT8iCtDA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-28T12:25:27.498051Z"},"content_sha256":"ae2cf261d901326fbebbf139f4484acd93a11ff8d66cdb932d37a525db08e6c5","schema_version":"1.0","event_id":"sha256:ae2cf261d901326fbebbf139f4484acd93a11ff8d66cdb932d37a525db08e6c5"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/6UPZHYLIQVVI4V3MNEVEEQ6K3R/bundle.json","state_url":"https://pith.science/pith/6UPZHYLIQVVI4V3MNEVEEQ6K3R/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/6UPZHYLIQVVI4V3MNEVEEQ6K3R/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":"2026-06-28T12:25:27Z","links":{"resolver":"https://pith.science/pith/6UPZHYLIQVVI4V3MNEVEEQ6K3R","bundle":"https://pith.science/pith/6UPZHYLIQVVI4V3MNEVEEQ6K3R/bundle.json","state":"https://pith.science/pith/6UPZHYLIQVVI4V3MNEVEEQ6K3R/state.json","well_known_bundle":"https://pith.science/.well-known/pith/6UPZHYLIQVVI4V3MNEVEEQ6K3R/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:6UPZHYLIQVVI4V3MNEVEEQ6K3R","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":"00fc97d49b387fa6356386c86f9cf88e2553674bdf80fe9d1deca4870ba27994","cross_cats_sorted":["math.DG","math.GR","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-10-03T23:54:41Z","title_canon_sha256":"237a9f92381973a0a27c96f027826d5b97e7687fc7c5fbcfc5b3ecc744e68708"},"schema_version":"1.0","source":{"id":"1310.1136","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1310.1136","created_at":"2026-05-18T02:44:31Z"},{"alias_kind":"arxiv_version","alias_value":"1310.1136v2","created_at":"2026-05-18T02:44:31Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1310.1136","created_at":"2026-05-18T02:44:31Z"},{"alias_kind":"pith_short_12","alias_value":"6UPZHYLIQVVI","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_16","alias_value":"6UPZHYLIQVVI4V3M","created_at":"2026-05-18T12:27:36Z"},{"alias_kind":"pith_short_8","alias_value":"6UPZHYLI","created_at":"2026-05-18T12:27:36Z"}],"graph_snapshots":[{"event_id":"sha256:ae2cf261d901326fbebbf139f4484acd93a11ff8d66cdb932d37a525db08e6c5","target":"graph","created_at":"2026-05-18T02:44:31Z","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":"Given a closed smooth manifold M which carries a positive scalar curvature metric, one can associate an abelian group P(M) to the space of positive scalar curvature metrics on this manifold. The group of all diffeomorphisms of the manifold naturally acts on P(M). The moduli group of positive scalar curvature metrics is defined to be the quotient abelian group of this action, i.e. the coinvariant of the action. The moduli group measures the size of the moduli space of positive scalar curvature metrics on M. In this paper, we use the higher rho invariant and the finite part of the K-theory of th","authors_text":"Guoliang Yu, Zhizhang Xie","cross_cats":["math.DG","math.GR","math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-10-03T23:54:41Z","title":"Higher rho invariants and the moduli space of positive scalar curvature metrics"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.1136","kind":"arxiv","version":2},"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":"sha256:110ecedbe9950b8d4de7e600df483ee91ecb5f79c176e0ebe904e987ece2dbea","target":"record","created_at":"2026-05-18T02:44:31Z","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":"00fc97d49b387fa6356386c86f9cf88e2553674bdf80fe9d1deca4870ba27994","cross_cats_sorted":["math.DG","math.GR","math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2013-10-03T23:54:41Z","title_canon_sha256":"237a9f92381973a0a27c96f027826d5b97e7687fc7c5fbcfc5b3ecc744e68708"},"schema_version":"1.0","source":{"id":"1310.1136","kind":"arxiv","version":2}},"canonical_sha256":"f51f93e168856a8e576c692a4243cadc7d39a8ece5e504dd0e3fe4a4235dc723","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"f51f93e168856a8e576c692a4243cadc7d39a8ece5e504dd0e3fe4a4235dc723","first_computed_at":"2026-05-18T02:44:31.888551Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:44:31.888551Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"iL7pqGswgDES3ezMn9k3gVbZe7ekx844blmavZqgfzVrv1niAm3LSyGhm1T83g3KbgXwcfE1DXtw/OrVRgRlCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:44:31.889116Z","signed_message":"canonical_sha256_bytes"},"source_id":"1310.1136","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:110ecedbe9950b8d4de7e600df483ee91ecb5f79c176e0ebe904e987ece2dbea","sha256:ae2cf261d901326fbebbf139f4484acd93a11ff8d66cdb932d37a525db08e6c5"],"state_sha256":"4abf9dff435dd35766b43f6fcfc053dba632d90f4c1a3484d1e88d50943302c4"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"h0wQGh/pb7xpbYAkCJWvHbchH5bMJ8jR0yGwo/VBaBSEdlKO+gqAcbYaGYrgyW/Z+8x/kqwSaKOPeOxM0VXACA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-28T12:25:27.500041Z","bundle_sha256":"c98a0f749e0e33501652e349eac9106cd46cbe958b2b0fb5a208a6e9ec53abec"}}