{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2013:RMX3UW52NWJIYD5XPWBZCPPDBP","short_pith_number":"pith:RMX3UW52","canonical_record":{"source":{"id":"1307.4604","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-07-17T12:55:55Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"426ca216385a274edf86731a78779ad55783b3b5e50e1daafa47725ea148fb82","abstract_canon_sha256":"691fe30a15a42e3a6ae4888bf398e94498f4df6b9c3375f12c9f32cef0ba8d97"},"schema_version":"1.0"},"canonical_sha256":"8b2fba5bba6d928c0fb77d83913de30bdc1de8dfa8821352011266dc42c9610b","source":{"kind":"arxiv","id":"1307.4604","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.4604","created_at":"2026-05-18T03:18:17Z"},{"alias_kind":"arxiv_version","alias_value":"1307.4604v1","created_at":"2026-05-18T03:18:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.4604","created_at":"2026-05-18T03:18:17Z"},{"alias_kind":"pith_short_12","alias_value":"RMX3UW52NWJI","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"RMX3UW52NWJIYD5X","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"RMX3UW52","created_at":"2026-05-18T12:27:59Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2013:RMX3UW52NWJIYD5XPWBZCPPDBP","target":"record","payload":{"canonical_record":{"source":{"id":"1307.4604","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-07-17T12:55:55Z","cross_cats_sorted":["math.SG"],"title_canon_sha256":"426ca216385a274edf86731a78779ad55783b3b5e50e1daafa47725ea148fb82","abstract_canon_sha256":"691fe30a15a42e3a6ae4888bf398e94498f4df6b9c3375f12c9f32cef0ba8d97"},"schema_version":"1.0"},"canonical_sha256":"8b2fba5bba6d928c0fb77d83913de30bdc1de8dfa8821352011266dc42c9610b","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:18:17.567658Z","signature_b64":"SJBjqC9/pxymTHeGA51EzKr9eHXkTm18ptOPwgPvzAtSZenJqSrmqMyE/MlhuDVnIXjljTDgaUHAs23MG34FAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8b2fba5bba6d928c0fb77d83913de30bdc1de8dfa8821352011266dc42c9610b","last_reissued_at":"2026-05-18T03:18:17.566989Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:18:17.566989Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1307.4604","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":"2026-05-18T03:18:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"vPbuGiqXSkfhTVAMD+oMYJsTuRMI6buAx5Mr4hSTc+mWHv5ABQ7JF3/9NV6exQEG5MfVN1qoTT73Yk1hSx94Cw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T15:29:37.403980Z"},"content_sha256":"a3c31d20163234ccdc7628430e42aeaa73db7b5a8d20135eab858953611d927e","schema_version":"1.0","event_id":"sha256:a3c31d20163234ccdc7628430e42aeaa73db7b5a8d20135eab858953611d927e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2013:RMX3UW52NWJIYD5XPWBZCPPDBP","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Dirac spectral flow on contact three manifolds I: eigensection estimates and spectral asymmetry","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SG"],"primary_cat":"math.DG","authors_text":"Chung-Jun Tsai","submitted_at":"2013-07-17T12:55:55Z","abstract_excerpt":"Let $Y$ be a compact, oriented 3-manifold with a contact form $a$ and a metric $ds^2$. Suppose that $F\\to Y$ is a principal bundle with structure group $U(2) = SU(2)\\times_{\\pm1}S^1$ such that $F/S^1$ is the principal SO(3) bundle of orthonormal frames for $TY$. A unitary connection $A_0$ on the Hermitian line bundle $F\\times_{\\det U(2)}\\mathbb{C}$ determines a self-adjoint Dirac operator $D_0$ on the $\\mathbb{C}^2$-bundle $F\\times_{U(2)}\\mathbb{C}^2$.\n  The contact form $a$ can be used to perturb the connection $A_0$ by $A_0-ira$. This associates a one parameter family of Dirac operators $D_r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4604","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":"2026-05-18T03:18:17Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"si4YmBNxyw33lQU0ZDwsKagSk7Z5U9wB40xmL4JX9XTpgKD7fYDtY2FMQIU/YLRmrl7pMs6I+5eKxDiZnM3bCg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-07-02T15:29:37.404342Z"},"content_sha256":"844e0d4de46541117d86f318e00ab17b6aad9898a239399b9cc357718c8bf9f6","schema_version":"1.0","event_id":"sha256:844e0d4de46541117d86f318e00ab17b6aad9898a239399b9cc357718c8bf9f6"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/RMX3UW52NWJIYD5XPWBZCPPDBP/bundle.json","state_url":"https://pith.science/pith/RMX3UW52NWJIYD5XPWBZCPPDBP/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/RMX3UW52NWJIYD5XPWBZCPPDBP/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":"2026-07-02T15:29:37Z","links":{"resolver":"https://pith.science/pith/RMX3UW52NWJIYD5XPWBZCPPDBP","bundle":"https://pith.science/pith/RMX3UW52NWJIYD5XPWBZCPPDBP/bundle.json","state":"https://pith.science/pith/RMX3UW52NWJIYD5XPWBZCPPDBP/state.json","well_known_bundle":"https://pith.science/.well-known/pith/RMX3UW52NWJIYD5XPWBZCPPDBP/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:RMX3UW52NWJIYD5XPWBZCPPDBP","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":"691fe30a15a42e3a6ae4888bf398e94498f4df6b9c3375f12c9f32cef0ba8d97","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-07-17T12:55:55Z","title_canon_sha256":"426ca216385a274edf86731a78779ad55783b3b5e50e1daafa47725ea148fb82"},"schema_version":"1.0","source":{"id":"1307.4604","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1307.4604","created_at":"2026-05-18T03:18:17Z"},{"alias_kind":"arxiv_version","alias_value":"1307.4604v1","created_at":"2026-05-18T03:18:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.4604","created_at":"2026-05-18T03:18:17Z"},{"alias_kind":"pith_short_12","alias_value":"RMX3UW52NWJI","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_16","alias_value":"RMX3UW52NWJIYD5X","created_at":"2026-05-18T12:27:59Z"},{"alias_kind":"pith_short_8","alias_value":"RMX3UW52","created_at":"2026-05-18T12:27:59Z"}],"graph_snapshots":[{"event_id":"sha256:844e0d4de46541117d86f318e00ab17b6aad9898a239399b9cc357718c8bf9f6","target":"graph","created_at":"2026-05-18T03:18:17Z","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":"Let $Y$ be a compact, oriented 3-manifold with a contact form $a$ and a metric $ds^2$. Suppose that $F\\to Y$ is a principal bundle with structure group $U(2) = SU(2)\\times_{\\pm1}S^1$ such that $F/S^1$ is the principal SO(3) bundle of orthonormal frames for $TY$. A unitary connection $A_0$ on the Hermitian line bundle $F\\times_{\\det U(2)}\\mathbb{C}$ determines a self-adjoint Dirac operator $D_0$ on the $\\mathbb{C}^2$-bundle $F\\times_{U(2)}\\mathbb{C}^2$.\n  The contact form $a$ can be used to perturb the connection $A_0$ by $A_0-ira$. This associates a one parameter family of Dirac operators $D_r","authors_text":"Chung-Jun Tsai","cross_cats":["math.SG"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-07-17T12:55:55Z","title":"Dirac spectral flow on contact three manifolds I: eigensection estimates and spectral asymmetry"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.4604","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:a3c31d20163234ccdc7628430e42aeaa73db7b5a8d20135eab858953611d927e","target":"record","created_at":"2026-05-18T03:18:17Z","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":"691fe30a15a42e3a6ae4888bf398e94498f4df6b9c3375f12c9f32cef0ba8d97","cross_cats_sorted":["math.SG"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2013-07-17T12:55:55Z","title_canon_sha256":"426ca216385a274edf86731a78779ad55783b3b5e50e1daafa47725ea148fb82"},"schema_version":"1.0","source":{"id":"1307.4604","kind":"arxiv","version":1}},"canonical_sha256":"8b2fba5bba6d928c0fb77d83913de30bdc1de8dfa8821352011266dc42c9610b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8b2fba5bba6d928c0fb77d83913de30bdc1de8dfa8821352011266dc42c9610b","first_computed_at":"2026-05-18T03:18:17.566989Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:18:17.566989Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SJBjqC9/pxymTHeGA51EzKr9eHXkTm18ptOPwgPvzAtSZenJqSrmqMyE/MlhuDVnIXjljTDgaUHAs23MG34FAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:18:17.567658Z","signed_message":"canonical_sha256_bytes"},"source_id":"1307.4604","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a3c31d20163234ccdc7628430e42aeaa73db7b5a8d20135eab858953611d927e","sha256:844e0d4de46541117d86f318e00ab17b6aad9898a239399b9cc357718c8bf9f6"],"state_sha256":"0c8b5e8ba0411de33ff2446c7d968aa547fd0ccc632a2627fe92c30051a28a21"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"ryJemMmu9lyM0Jf1Xv0VxJmCBSNR+Oy3HYfWA+sU/zfAyTzoK1seIkJg/r+gC8po7Erkp4ESSbHExf9tkoqKDw==","signed_message":"bundle_sha256_bytes","signed_at":"2026-07-02T15:29:37.406246Z","bundle_sha256":"3b34097c22711165c4f8078e94bfaebb891080b5bc9c7debb09ae8dd5d88dae6"}}