{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2004:F3ZHV7TVMBA4NVUSBD7H6HUZ3D","short_pith_number":"pith:F3ZHV7TV","canonical_record":{"source":{"id":"math/0412191","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2004-12-09T16:14:12Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"749809ab1adcf65f1e47b828d5c54db06d5f385c7ccb9a9f34214e4ca62a054f","abstract_canon_sha256":"449006e52448b031012c949aac790dbbc3e398b75f924ad2919c83e912744c88"},"schema_version":"1.0"},"canonical_sha256":"2ef27afe756041c6d69208fe7f1e99d8c6ff8434e0a47271dacb3e12e221afff","source":{"kind":"arxiv","id":"math/0412191","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0412191","created_at":"2026-05-18T02:37:59Z"},{"alias_kind":"arxiv_version","alias_value":"math/0412191v3","created_at":"2026-05-18T02:37:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0412191","created_at":"2026-05-18T02:37:59Z"},{"alias_kind":"pith_short_12","alias_value":"F3ZHV7TVMBA4","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"F3ZHV7TVMBA4NVUS","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"F3ZHV7TV","created_at":"2026-05-18T12:25:52Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2004:F3ZHV7TVMBA4NVUSBD7H6HUZ3D","target":"record","payload":{"canonical_record":{"source":{"id":"math/0412191","kind":"arxiv","version":3},"metadata":{"license":"","primary_cat":"math.GT","submitted_at":"2004-12-09T16:14:12Z","cross_cats_sorted":["math.DG"],"title_canon_sha256":"749809ab1adcf65f1e47b828d5c54db06d5f385c7ccb9a9f34214e4ca62a054f","abstract_canon_sha256":"449006e52448b031012c949aac790dbbc3e398b75f924ad2919c83e912744c88"},"schema_version":"1.0"},"canonical_sha256":"2ef27afe756041c6d69208fe7f1e99d8c6ff8434e0a47271dacb3e12e221afff","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:37:59.849046Z","signature_b64":"h7cDgpQStTnxhiGgsKHKWEYiGYdsT+MzpEQbLOBXaccp422pJH12aU4eoT9KzK40QXdY6DCZOz/fJmUGp5AZDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2ef27afe756041c6d69208fe7f1e99d8c6ff8434e0a47271dacb3e12e221afff","last_reissued_at":"2026-05-18T02:37:59.848653Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:37:59.848653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/0412191","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T02:37:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"W7P5zX4pZ1CrYfvBiVKtHg/4vMV8MyXKXc/fqawtwe/Ug2hdOmVFdzRWwr2elZddU+kc0qfzLgs6/4Pk5Xd4DA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T11:02:00.495211Z"},"content_sha256":"aaff5fa41604e5f16f4475c8e90034c0f8cb213ea8cc40d095501adc952a897f","schema_version":"1.0","event_id":"sha256:aaff5fa41604e5f16f4475c8e90034c0f8cb213ea8cc40d095501adc952a897f"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2004:F3ZHV7TVMBA4NVUSBD7H6HUZ3D","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"A splitting formula for the spectral flow of the odd signature operator on 3-manifolds coupled to a path of SU(2) connections","license":"","headline":"","cross_cats":["math.DG"],"primary_cat":"math.GT","authors_text":"Benjamin Himpel","submitted_at":"2004-12-09T16:14:12Z","abstract_excerpt":"We establish a splitting formula for the spectral flow of the odd signature operator on a closed 3-manifold M coupled to a path of SU(2) connections, provided M = S cup X, where S is the solid torus. It describes the spectral flow on M in terms of the spectral flow on S, the spectral flow on X (with certain Atiyah-Patodi-Singer boundary conditions), and two correction terms which depend only on the endpoints.\n  Our result improves on other splitting theorems by removing assumptions on the non-resonance level of the odd signature operator or the dimension of the kernel of the tangential operato"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0412191","kind":"arxiv","version":3},"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":"2026-05-18T02:37:59Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"4XS3iHaJjUebU+quEF/hHc0IjyURFvrFqi90rNPfQSFA/CjkRn9mHnAGLez7d7l7jXx3QQHsXYUd+kCEQ+WiBQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-24T11:02:00.495625Z"},"content_sha256":"a79a6634fb09f3b5568d66fa20c7b5768dd2c7f5af24dadcc43dd12d3e876f08","schema_version":"1.0","event_id":"sha256:a79a6634fb09f3b5568d66fa20c7b5768dd2c7f5af24dadcc43dd12d3e876f08"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/F3ZHV7TVMBA4NVUSBD7H6HUZ3D/bundle.json","state_url":"https://pith.science/pith/F3ZHV7TVMBA4NVUSBD7H6HUZ3D/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/F3ZHV7TVMBA4NVUSBD7H6HUZ3D/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":"2026-06-24T11:02:00Z","links":{"resolver":"https://pith.science/pith/F3ZHV7TVMBA4NVUSBD7H6HUZ3D","bundle":"https://pith.science/pith/F3ZHV7TVMBA4NVUSBD7H6HUZ3D/bundle.json","state":"https://pith.science/pith/F3ZHV7TVMBA4NVUSBD7H6HUZ3D/state.json","well_known_bundle":"https://pith.science/.well-known/pith/F3ZHV7TVMBA4NVUSBD7H6HUZ3D/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2004:F3ZHV7TVMBA4NVUSBD7H6HUZ3D","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":"449006e52448b031012c949aac790dbbc3e398b75f924ad2919c83e912744c88","cross_cats_sorted":["math.DG"],"license":"","primary_cat":"math.GT","submitted_at":"2004-12-09T16:14:12Z","title_canon_sha256":"749809ab1adcf65f1e47b828d5c54db06d5f385c7ccb9a9f34214e4ca62a054f"},"schema_version":"1.0","source":{"id":"math/0412191","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/0412191","created_at":"2026-05-18T02:37:59Z"},{"alias_kind":"arxiv_version","alias_value":"math/0412191v3","created_at":"2026-05-18T02:37:59Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/0412191","created_at":"2026-05-18T02:37:59Z"},{"alias_kind":"pith_short_12","alias_value":"F3ZHV7TVMBA4","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_16","alias_value":"F3ZHV7TVMBA4NVUS","created_at":"2026-05-18T12:25:52Z"},{"alias_kind":"pith_short_8","alias_value":"F3ZHV7TV","created_at":"2026-05-18T12:25:52Z"}],"graph_snapshots":[{"event_id":"sha256:a79a6634fb09f3b5568d66fa20c7b5768dd2c7f5af24dadcc43dd12d3e876f08","target":"graph","created_at":"2026-05-18T02:37:59Z","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 establish a splitting formula for the spectral flow of the odd signature operator on a closed 3-manifold M coupled to a path of SU(2) connections, provided M = S cup X, where S is the solid torus. It describes the spectral flow on M in terms of the spectral flow on S, the spectral flow on X (with certain Atiyah-Patodi-Singer boundary conditions), and two correction terms which depend only on the endpoints.\n  Our result improves on other splitting theorems by removing assumptions on the non-resonance level of the odd signature operator or the dimension of the kernel of the tangential operato","authors_text":"Benjamin Himpel","cross_cats":["math.DG"],"headline":"","license":"","primary_cat":"math.GT","submitted_at":"2004-12-09T16:14:12Z","title":"A splitting formula for the spectral flow of the odd signature operator on 3-manifolds coupled to a path of SU(2) connections"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0412191","kind":"arxiv","version":3},"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:aaff5fa41604e5f16f4475c8e90034c0f8cb213ea8cc40d095501adc952a897f","target":"record","created_at":"2026-05-18T02:37:59Z","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":"449006e52448b031012c949aac790dbbc3e398b75f924ad2919c83e912744c88","cross_cats_sorted":["math.DG"],"license":"","primary_cat":"math.GT","submitted_at":"2004-12-09T16:14:12Z","title_canon_sha256":"749809ab1adcf65f1e47b828d5c54db06d5f385c7ccb9a9f34214e4ca62a054f"},"schema_version":"1.0","source":{"id":"math/0412191","kind":"arxiv","version":3}},"canonical_sha256":"2ef27afe756041c6d69208fe7f1e99d8c6ff8434e0a47271dacb3e12e221afff","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2ef27afe756041c6d69208fe7f1e99d8c6ff8434e0a47271dacb3e12e221afff","first_computed_at":"2026-05-18T02:37:59.848653Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:37:59.848653Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"h7cDgpQStTnxhiGgsKHKWEYiGYdsT+MzpEQbLOBXaccp422pJH12aU4eoT9KzK40QXdY6DCZOz/fJmUGp5AZDA==","signature_status":"signed_v1","signed_at":"2026-05-18T02:37:59.849046Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/0412191","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:aaff5fa41604e5f16f4475c8e90034c0f8cb213ea8cc40d095501adc952a897f","sha256:a79a6634fb09f3b5568d66fa20c7b5768dd2c7f5af24dadcc43dd12d3e876f08"],"state_sha256":"5450c2a2c973a976b2609d9f5c08a2d5c6e9e8ec5241effe90c740b55711d035"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"2z6o/wku32FiM07fOHj8ugj6thItSMckrZTb1SuKYWRcGaqLkyT0yNQemck0Qc480z6pdtR3K19TR00EIySnDQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-24T11:02:00.498122Z","bundle_sha256":"045053ace0d58c63b5075f389de71fd0a50e1e84c1cb8b40378f35defa081aaa"}}