{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:NEZQNXA7X7NURD56L6WJ2YHQ4N","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":"05989cad850cd96280ecab674bd6bf1aa9e72fe42988787a76e3067cb45c2860","cross_cats_sorted":["math.AP","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-03-13T13:16:36Z","title_canon_sha256":"a74412098b2017d4a9db8a45ee827ff277e77ebe0223b1da07cf87836443b7a7"},"schema_version":"1.0","source":{"id":"1203.2793","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1203.2793","created_at":"2026-05-18T03:22:06Z"},{"alias_kind":"arxiv_version","alias_value":"1203.2793v2","created_at":"2026-05-18T03:22:06Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.2793","created_at":"2026-05-18T03:22:06Z"},{"alias_kind":"pith_short_12","alias_value":"NEZQNXA7X7NU","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_16","alias_value":"NEZQNXA7X7NURD56","created_at":"2026-05-18T12:27:16Z"},{"alias_kind":"pith_short_8","alias_value":"NEZQNXA7","created_at":"2026-05-18T12:27:16Z"}],"graph_snapshots":[{"event_id":"sha256:a4547829d67a321f482100a69af0d60ebd872ab6d3c3bd51a89866fbb0aaf813","target":"graph","created_at":"2026-05-18T03:22:06Z","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 prove a gluing formula for the analytic torsion on non-compact (i.e. singular) riemannian manifolds. Let M= U\\cup M_1, where M_1 is a compact manifold with boundary and U represents a model of the singularity. For general elliptic operators we formulate a criterion, which can be checked solely on U, for the existence of a global heat expansion, in particular for the existence of the analytic torsion in case of the Laplace operator. The main result then is the gluing formula for the analytic torsion. Here, decompositions M=M_1\\cup_W M_2 along any compact closed hypersurface W with M_1, M_2 b","authors_text":"Matthias Lesch","cross_cats":["math.AP","math.DG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-03-13T13:16:36Z","title":"A gluing formula for the analytic torsion on singular spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.2793","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":"sha256:72413a3b8516e1dd218e1405f1efd3298174739a33e6f1c276c02dd20dcea48c","target":"record","created_at":"2026-05-18T03:22:06Z","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":"05989cad850cd96280ecab674bd6bf1aa9e72fe42988787a76e3067cb45c2860","cross_cats_sorted":["math.AP","math.DG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.SP","submitted_at":"2012-03-13T13:16:36Z","title_canon_sha256":"a74412098b2017d4a9db8a45ee827ff277e77ebe0223b1da07cf87836443b7a7"},"schema_version":"1.0","source":{"id":"1203.2793","kind":"arxiv","version":2}},"canonical_sha256":"693306dc1fbfdb488fbe5fac9d60f0e37e7a5f14349dfc836b546b5a1e370f37","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"693306dc1fbfdb488fbe5fac9d60f0e37e7a5f14349dfc836b546b5a1e370f37","first_computed_at":"2026-05-18T03:22:06.264757Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:22:06.264757Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OeODPQllimFbtBmoam7btuMxxFzNz4ebym8TzvCLlCUSnwOScRtPwT8khY7xl7y0pL7qnKQ1rETaHlPyutK6Aw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:22:06.265278Z","signed_message":"canonical_sha256_bytes"},"source_id":"1203.2793","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:72413a3b8516e1dd218e1405f1efd3298174739a33e6f1c276c02dd20dcea48c","sha256:a4547829d67a321f482100a69af0d60ebd872ab6d3c3bd51a89866fbb0aaf813"],"state_sha256":"4b7d7545c22769fe9920d49462c6275c3a40ae51fc46a393fec7e459215c5bb5"}