{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2011:GM3B3ZGSUFK6NLUASI6PGFF77S","short_pith_number":"pith:GM3B3ZGS","canonical_record":{"source":{"id":"1112.0989","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-12-05T16:49:12Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"326a6a1bf5f1b2e271f1a3cd18e2865fe162c33a81ebe095cc96ae5bc5cdac3a","abstract_canon_sha256":"3b0e88a0439bb1c5580cd5743e2ec0829c764fd8db8f41c90675e93df55bb8ac"},"schema_version":"1.0"},"canonical_sha256":"33361de4d2a155e6ae80923cf314bffcb8be692653c5b9f78311fb44b685bcde","source":{"kind":"arxiv","id":"1112.0989","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.0989","created_at":"2026-05-18T04:06:57Z"},{"alias_kind":"arxiv_version","alias_value":"1112.0989v1","created_at":"2026-05-18T04:06:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.0989","created_at":"2026-05-18T04:06:57Z"},{"alias_kind":"pith_short_12","alias_value":"GM3B3ZGSUFK6","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GM3B3ZGSUFK6NLUA","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GM3B3ZGS","created_at":"2026-05-18T12:26:30Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2011:GM3B3ZGSUFK6NLUASI6PGFF77S","target":"record","payload":{"canonical_record":{"source":{"id":"1112.0989","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-12-05T16:49:12Z","cross_cats_sorted":["math.KT"],"title_canon_sha256":"326a6a1bf5f1b2e271f1a3cd18e2865fe162c33a81ebe095cc96ae5bc5cdac3a","abstract_canon_sha256":"3b0e88a0439bb1c5580cd5743e2ec0829c764fd8db8f41c90675e93df55bb8ac"},"schema_version":"1.0"},"canonical_sha256":"33361de4d2a155e6ae80923cf314bffcb8be692653c5b9f78311fb44b685bcde","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:06:57.314362Z","signature_b64":"ZKOQoolIILRZHqm/J/JbzMchiaO4GyI48uSWU1/RcK/LnVw0f2zdTegilpaz/PmfZsHrXHO7VlKA3Rc+VBfaBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"33361de4d2a155e6ae80923cf314bffcb8be692653c5b9f78311fb44b685bcde","last_reissued_at":"2026-05-18T04:06:57.313791Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:06:57.313791Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1112.0989","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":"2026-05-18T04:06:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CZUsCobZiGO8yquRfdXbj85iiftcZlcBwU3hWuLnagPnBpB2KwJaZG1vU7qKE/IxlTyle1OmEpn2KUhFUsGYCw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T01:30:26.681208Z"},"content_sha256":"bb2eea0fa5e03315fc785c800dc2bb21082e8b272c71a23b892c65fac67726db","schema_version":"1.0","event_id":"sha256:bb2eea0fa5e03315fc785c800dc2bb21082e8b272c71a23b892c65fac67726db"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2011:GM3B3ZGSUFK6NLUASI6PGFF77S","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"The signature package on Witt spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.KT"],"primary_cat":"math.DG","authors_text":"Eric Leichtnam, Paolo Piazza, Pierre Albin, Rafe Mazzeo","submitted_at":"2011-12-05T16:49:12Z","abstract_excerpt":"In this paper we prove a variety of results about the signature operator on Witt spaces. First, we give a parametrix construction for the signature operator on any compact, oriented, stratified pseudomanifold X which satisfies the Witt condition. This construction, which is inductive over the `depth' of the singularity, is then used to show that the signature operator is essentially self-adjoint and has discrete spectrum of finite multiplicity, so that its index -- the analytic signature of X -- is well-defined. This provides an alternate approach to some well-known results due to Cheeger. We "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0989","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":"2026-05-18T04:06:57Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"uhl3rue+48PfKnZYNULk00TSkZiYTnGba3bs/tOIODSPPWVVf0aVGyLpvB+RLukJNkLNAs6RkSZzwACe775FCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-05T01:30:26.681904Z"},"content_sha256":"5e1adc40758038012e3df581218c33a95d427498493439c1c485c6a908909da9","schema_version":"1.0","event_id":"sha256:5e1adc40758038012e3df581218c33a95d427498493439c1c485c6a908909da9"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/GM3B3ZGSUFK6NLUASI6PGFF77S/bundle.json","state_url":"https://pith.science/pith/GM3B3ZGSUFK6NLUASI6PGFF77S/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/GM3B3ZGSUFK6NLUASI6PGFF77S/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":"2026-06-05T01:30:26Z","links":{"resolver":"https://pith.science/pith/GM3B3ZGSUFK6NLUASI6PGFF77S","bundle":"https://pith.science/pith/GM3B3ZGSUFK6NLUASI6PGFF77S/bundle.json","state":"https://pith.science/pith/GM3B3ZGSUFK6NLUASI6PGFF77S/state.json","well_known_bundle":"https://pith.science/.well-known/pith/GM3B3ZGSUFK6NLUASI6PGFF77S/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:GM3B3ZGSUFK6NLUASI6PGFF77S","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":"3b0e88a0439bb1c5580cd5743e2ec0829c764fd8db8f41c90675e93df55bb8ac","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-12-05T16:49:12Z","title_canon_sha256":"326a6a1bf5f1b2e271f1a3cd18e2865fe162c33a81ebe095cc96ae5bc5cdac3a"},"schema_version":"1.0","source":{"id":"1112.0989","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1112.0989","created_at":"2026-05-18T04:06:57Z"},{"alias_kind":"arxiv_version","alias_value":"1112.0989v1","created_at":"2026-05-18T04:06:57Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.0989","created_at":"2026-05-18T04:06:57Z"},{"alias_kind":"pith_short_12","alias_value":"GM3B3ZGSUFK6","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_16","alias_value":"GM3B3ZGSUFK6NLUA","created_at":"2026-05-18T12:26:30Z"},{"alias_kind":"pith_short_8","alias_value":"GM3B3ZGS","created_at":"2026-05-18T12:26:30Z"}],"graph_snapshots":[{"event_id":"sha256:5e1adc40758038012e3df581218c33a95d427498493439c1c485c6a908909da9","target":"graph","created_at":"2026-05-18T04:06:57Z","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":"In this paper we prove a variety of results about the signature operator on Witt spaces. First, we give a parametrix construction for the signature operator on any compact, oriented, stratified pseudomanifold X which satisfies the Witt condition. This construction, which is inductive over the `depth' of the singularity, is then used to show that the signature operator is essentially self-adjoint and has discrete spectrum of finite multiplicity, so that its index -- the analytic signature of X -- is well-defined. This provides an alternate approach to some well-known results due to Cheeger. We ","authors_text":"Eric Leichtnam, Paolo Piazza, Pierre Albin, Rafe Mazzeo","cross_cats":["math.KT"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-12-05T16:49:12Z","title":"The signature package on Witt spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0989","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:bb2eea0fa5e03315fc785c800dc2bb21082e8b272c71a23b892c65fac67726db","target":"record","created_at":"2026-05-18T04:06:57Z","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":"3b0e88a0439bb1c5580cd5743e2ec0829c764fd8db8f41c90675e93df55bb8ac","cross_cats_sorted":["math.KT"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2011-12-05T16:49:12Z","title_canon_sha256":"326a6a1bf5f1b2e271f1a3cd18e2865fe162c33a81ebe095cc96ae5bc5cdac3a"},"schema_version":"1.0","source":{"id":"1112.0989","kind":"arxiv","version":1}},"canonical_sha256":"33361de4d2a155e6ae80923cf314bffcb8be692653c5b9f78311fb44b685bcde","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"33361de4d2a155e6ae80923cf314bffcb8be692653c5b9f78311fb44b685bcde","first_computed_at":"2026-05-18T04:06:57.313791Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:06:57.313791Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"ZKOQoolIILRZHqm/J/JbzMchiaO4GyI48uSWU1/RcK/LnVw0f2zdTegilpaz/PmfZsHrXHO7VlKA3Rc+VBfaBw==","signature_status":"signed_v1","signed_at":"2026-05-18T04:06:57.314362Z","signed_message":"canonical_sha256_bytes"},"source_id":"1112.0989","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:bb2eea0fa5e03315fc785c800dc2bb21082e8b272c71a23b892c65fac67726db","sha256:5e1adc40758038012e3df581218c33a95d427498493439c1c485c6a908909da9"],"state_sha256":"e3abc60933aaa5e9d150585ce946ccbb86a2f909081c0baffc8433400c2192c3"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"LbUPKKMhstxws5h75kSBILtO60FqUR5kTTMbV2Le2rshK5H2oI1er7ozPTaCDRYS8joQHYwlNH+WJ8g3Cr5ABQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-05T01:30:26.686008Z","bundle_sha256":"82141b6eea9cb1ca8194dd89656cd23b49bc4bdb178ec5d1356ffba86a655384"}}